Complete Units, Dimensions And Error | JEE 2025 | All Concepts & PYQs | Shreyas Sir

hello my dear Lions welcome welcome to the first lecture of our Ro series which is for j25 and J 2026 so all the students a very warm w namaskaram and y welcome welcome welcome nice to see all of you hello nari aan abinav hello dhani hello hello hello good evening my dear Warriors now this Roar series like I introduced yesterday is a full-fledged YouTube series which is one of its kind first of all it's in pure English number two uh these lectures are going to be detailed with three levels of questions level one which is going to be basic then level two which is going to be you know Mains level here and there and then level three which is going to push you beyond means till Advanced so my dear Warriors apart from the different questions practice we will start with the theory and then we will see the question Theory and then the questions so that you have adequate command over the subject not just that you will get the entire handwritten notes of whatever I'm going to do today in The Jungle Book the link of the Jungle Book is there in the description box which is a nice nice sheet arranged for all of you where you will get all the PDFs notes lectures everything systematically arranged and over a period of time this Jungle Book will be one source of your you know all the lectures at one place okay so let's get ready there are going to beqs of course and everything else will be shared in The Jungle Book as well as the telegram channel so in the comment section of this particular video you might be seeing you know the Jungle Book uh sorry the telegram Channel link so today we are starting off with units and dimensions and I'm pretty sure you are all excited just like the Tom cartoon out here but by the time you reach rotation I hope you do not become like this because it all starts with great excitement what matters is also whether you can carry it Forward hello Mohammad hello diali hello Kika hello Leah hello haran hello hanuma AB have already joined very good good evening good evening so the point is you start with good Jo should start with great energy but it should not die out so make yourself a promise that you know you probably have next 6 Months 8 months depending on which standard you are in to crack the J means you know set a Target watch these lectures Live recorded I don't know whether you might be watching it next year even year after that also so set the Target and complete these series of lectures you know as soon as possible we are going to be committed you need to show that commitment all right so my my name is Captain stas for those of you who do not know me teaching kids for a very long time more than 13 years now and sending these kids into the colleges and now it's your so NE 2024 sorry j 2024 was a successful year for all of us lots of students did really well and we are proud that we did so many sessions so many lectures for them that literally they were prepared for every exam which is on their way now it is your turn make the best use of this J English Channel which is one of its kind you will love not just the channels and the teachers but you'll also love the subject very soon in case you have not fallen in love okay so guys I've done my research from it Bombay did my graduation from an nagpur now it's your turn now so let's get set go smash the like button in case you haven't done that yet all right okay let's rooll all the warrior pandus all the warrior pandu whistle ping that's wpwp that's the hashtag which you're going to follow throughout the series wpwp right that's for your captain sh sir and you are the new Lions now who are going to Roar cool let's begin with the lecture and let's start with something called as the physical quantity now this whole chapter deals with physical quantities units dimensions and errors that is the flow of event for these uh for this particular lecture okay for this uh chapter which we are going to study here today we start with quantities we'll go to units Dimensions significant figures and rounding off and all of that and then we will go to basically errors and their combination now when we say a physical quantity a physical quantity is something which can be measured like for example if I ask you how excited you are you'll be like yes sir I'm very excited I can't measure that excitement I can't just say very excited is uh you know of this level low excitement is of this level I mean you cannot associate numbers with it I cannot even associate I have fever I have fever I'm feeling more feverish less feverish it's a very relative and subjective term but when I say I have 100° Fahrenheit fever versus I have 99 degre fenhe fever then because the temperature is used now or I'm associating it now with temperature which can be measured in numbers that's when it becomes a physical quantity so temperature is a physical quantity whereas fever is not a physical quantity similarly there are many such physical quantities like you have length mass time force velocity speed acceleration momentum field so many quantities are there around you right area volume density correct very good uh so kanishka we'll start with class 12th parallell this week we'll just do the basics so that we have some basic understanding then we'll do class 11th and 12th almost parall you will see that okay great now that any quantity which can be measured is called as a physical quantity this physical quantity can be classified into two types so whenever you have a physical quantity we can classify it into two categories one is basically called as fundamental quantity fundamental quantity versus something called as derived quantity derived quantity this is one way of organizing them or classifying them the second way is which we are going to study in the next lecture one is called as a scalar quantity the other one is called as a vector quantity most of you have dealt with scalers till your school level now vectors is the thing which you need to learn till in the J level we will learn about this in the other class there is a separate chapter only called as vectors and scales forget about it for now for now let's concentrate over here which is fundamental versus derived what is the meaning of the word fundamental fundamental the word itself says that it is very very basic it is very very basic or it is very very empirical empirical empirical means it is too low or very very like natural I mean it is like taken for granted like it has to be there it is very very very foundational level or basic level that is the meaning of empirical or basic so there are some entities which are very fundamental example length time Mass very very fundamental things any other things are dependent on these things any other thing is dependent on these things so those are called derived because are dependent they are dependent what are they dependent on they are dependent on these quantities they are dependent on these quantities I will give you a very very simple example which will make you understand this when I say when I say a fundamental quantity when I say a fundamental quantity very very basic quantity like Mass you can directly you know put it in a pan and measure it it's a so basic so fundamental right I can call mass as a fundamental quantity I take a scale and directly measure something and that means I can directly measure the length of the object I have a watch or a clock I look at the time directly I can measure it so that is basically another fundamental quantity now imagine imagine I talk about speed if I talk about speed for getting speed I need the quantity called as length by which I can measure the distance and I divide it with time so speed depends on length as well as time that is why it is a derived quantity that is why it is a derived quantity agree with this similarly even volume volume of something uh let's say a cube it's basically side into side one into side two into side three basically you take length of one side into length of the other side into length of the other side so length is Multiplied three times so I can think of the fundamental quantity of length coming three times so length cube right so volume becomes a derived quantity because it depends on the length in fact even the quantity like density density is also a derived quantity because it depends on mass and volume but volume itself depends on volume itself depends on length so it is length raised to three uh below and Mass on the top so all these are examples of derived or dependent quantities what are they dependent on the basic empirical things like Mass length time Etc correct we will come to charge also yes what do you think is charge is it a fundamental or is it a derived the thing is you the way the charge or you know currents have been defined it so happens that current is more fundamental in our system of choice that we have and charge is a derived quantity so yes you will see that it is the current which is the fundamental quantity because you will see later on in the chapter of magnetism how current is defined by you know placing two wires adjacent to each each other and measuring the force acting per unit length and all those things but current is fundamental and charge is derived because current is charge by time charge charge will be basically how much current is Flowing how much current is Flowing you multiply it with the time so you can see two dependent quantities fundamentals so this becomes a derived quantity this becomes a derived quantity understood my dear Warriors yeah yes current also depends on time but it is fundamental quantity how sir so it depends on how you choose as fundamental you know this is a very valid doubt Kevin why should speed be derived and you know length and time be fundamental I can say no no no no no wait a minute this is not fundamental and this is not derived in some another world Kevin's world like Kevin even asked a doubt length is velocity by time I can take and velocity as fundamental and then I can take length as derived quantity perfectly okay nothing wrong in it but that is in your Universe just like you have you know DC and Marvel Universe right same way in your world your line of thought in your Universe no issues but it has to be accepted widely so so all the scientists engineers mathematicians sat together and they thought okay let's decide which is fundamental which is derived or else everybody will say no for me this is fundamental this is derived so it is just a matter of historical convention that we assume length mass time current as fundamental quantity got it understood my dear Warriors yep yes there is a quantity called tensor initially see I mean you will see that in engineering and all that but in J physics you don't see anything about aners got it clear yep sharan we'll be solving level three questions which is J advaned level everybody with me understood the true difference between fundamental and derived who decided fundamental and derived quantities all of us just like we decided we are going to drive on the left side of the road one can question why only left side I can drive on the right side so we need to have some kind of rules that is the reason why we decided what is fundamental and what is derived based on a general you know um opinion okay scientific opinion great so we saw that there are two types of physical quantities physical quantities are the ones which you can measure there is a number associated with it unlike happiness which can't be measured and fundamental is very basic derived depends on the fundamental quantities now in our universe we have seven fundamental quantities scientists and Engineers saw all the things around us and they saw that many of these things depend on other things and if you assume these seven fundamental quantities everything and anything in this universe can be derived using these seven quantities there is nothing as of now at least there is nothing as of now which you cannot get using these seven quantities so what are those seven quantities I will come to it but also keep in mind there are also two supplementary what is the meaning of supplement you all have written board exams in your 10th or maybe some of you are droppers and written it in 12th you get a main booklet and you are a Topper or you are writing too much lengthy lengthy answers what do you go and ask the invigilator a supplement right you ask a supplement right so it's an additional thing right so same way scientists realize oh there are these seven fundamental quantities or and you can get any other quantity using these you know fundamental uh seven quantities then they realize oh wait a minute there are two additional ones but they are little bit special they needed they need some special treatment so they added two more supplements supplementary yes I additional wow some of you got 497 wow crazy awesome awesome yeah additional so same way these are additional quantities but they have some special thing or else somebody will ask sir why not then call it as nine fundamental quantities 7 + 2 is n no sir why chumma call it supplementary there is a special thing about that supplementary quantities we'll talk about it but for now let's see what are those basic seven fundamental quantities first one remember this length the length of an object second one how much matter is there Mass how much quantity of mass matter time how much time has gone elapsed what is the time yes electrical current which I was just telling you is a fundamental quantity temperature temperature in thermodynamics you'll see we measure the temperature of any body it is also a fundamental quantity light intensity you will see the Luminous intensity is also a fundamental quantity how intense that light is okay you will generally not see this in J but it is just there only in this chapter you will not see this luminous intensity in any other chapter otherwise quantity of substance yes you will see this not only in physics but also in chemistry so quantity of substance intensity of light temperature electrical current mass and length 1 2 3 4 5 6 7 by heart this and store it in your memory everyone with me everyone with me Shri Vishnu the class has already started yes okay clear very good kalash good evening athetic Kido everybody clear till this point very good very good awesome now what are the two additional supplements the two additional supplements are plain angle and and solid Angle now PL angle is something which you learn uh I mean at school level solid angle is something what you will learn probably in electrostatics and you know goss's law later on in 12th standard but just to give you a very vague idea of what is a plain angle versus a solid angle lot of people have this confusion plain angle is basically an angle in two Dimension you take any two lines you see what is the thing between them the thing between them is called as the angle which you call as the Plaine angle this is a angle in basically two Dimension obviously you can think what a solid will be it will be an angle in three dimension so now when you have two lines in that plane the thing between them is called as the angle in three dimension just visualize something which is encompassing or enclosing some you know object it could be anything else it could be just anything it could be as simple as this particular t-shirt okay just imagine uh you take a line and go along the boundary of this t-shirt you go along the boundary of this t-shirt okay or maybe you take this particular surface I don't know whether you can see it and you take a line and point it everywhere along the surface or the circumference okay you go from here you go like this like this so the thing which is there inside is called as the solid angle so you can see um this was that particular surface I hope you can see that this was that particular surface you take this line and slowly move it around this so this particular thing over here it is in three dimension that is called as the solid angle that is called as the solid angle visualize this in three dimension and you will see this later on that just like when you have an arc when you have an arc the length of an arc is basically radius times the angle you will soon see that if you have a patch if you have a surface then the area of that surface area of that surface will be square of the radius multiplied by multiplied by the solid angle multiplied by this is Oham symbol but this is I'm using the symbol for solid angle okay so just like length is radius into Theta then area of this is radius square into the solid angle that is how the solid angle is defined for now you just need to know this much it is more than enough just now you just need to know this much more than enough that's all angle in three dimension angle in two Dimension 2D means I just need two lines and in that plane what is the thing between them is the angle in 3D I will take a line and I will you know go along the circumference like this so the thing which is enclosed by this line inside that is called as the solid angle these are the two supplementary units it's the two supplementary units perfect so we have seen what is fundamental we have seen what is is derived derived I showed you so many examples guys force velocity Etc and you know the entire physics right from chapter two to the last chapter is just studying these physical quantities and I gave you all these examples of fundamental versus derived right over here only I guess where did it go yes fundamental versus derived I gave you a lot of examples right over here I can show you some more examples over here you can see this for example frequency is one by time one by time time is a fundamental frequency becomes dependent on time so it is a derived quantity force is mass into acceleration so force is a derived quantity work energy heat all are derived quantities pressure is force by area derived quantity power work by time again derived quantity charge is current into time again derived quantity so there are lot of derived quantity and your entire physics you just going to study these physical quantities throughout your physics electrical potential capacitance resistance conductance magnetic field magnetic flux inductance you can see so many quantities are there got it my dear Warriors don't worry about all these things I'm just giving you an example that this is what you're going to learn throughout physics shall we solve some questions ready for the first question on your screen ready for the first question question on your screen yep very good awesome it's raining everywhere Chennai Hyderabad Bangalore I can confirm that okay near my house too all right my dear Warriors so time for the first question on your screen which of the following is not a fundamental quantity which of the following is not very fundamental come on put up the answer in the chat box quickly okay come on my dear Warriors waiting waiting waiting for your chats quickly let me know the answer in the chat box what do you think it is is it a current is it B come on distance is it C which is heat or D which is temperature everybody saying C oh is it just C no it is not C it is c for Captain Shas it's not just C it's c for Captain Shas hopefully yes it is c for cap to C for Captain stas perfect not a fundamental quantity current is is a fundamental it is not derived charge is a derived quantity distance length definitely fundamental temperature I just told you temperature degree Fahrenheit Celsius however you measure it is fundamental heat depends on other things so guys it is a derived quantity not a fundamental quantity question was not a fundamental not that word not is very important so this was level one I think that level is not seen um I think somewhere over here I think next time I should put it on the top it is getting hidden over here I think so yeah it is hidden basically I'll show you what has happened in the PDF it will come because these things are there it is not being shown so this is the actual Google slide so which I make it into PDF and share it with you so over here if you see over here if you see it shows as level one now what is happening is when I use this note so all those things are getting hidden so when you get the actual PDF then you will probably see level one level two next time I'll make sure this is written over here I just realized it is getting hidden Okay cool so don't get scared sir did not solve level one level two level three oh my God okay it will be seen later on all right moving on now to units part why not a uh uh I just told you right over here what are the fundamental units fundamental units current these are assumed to be the fundamental everything else can be dependent on it like for example you can see over here charge electrical charge is current multiplied by time charge is a derived quantity got it okay not current current is assumed to be fundamental it's just by convention by history yeah I can actually move it is that I don't know how I can move it I don't want to waste the time over here now okay so not sure how to move this okay anyways okay let me not waste my time over there okay so what is this unit if I tell you if I tell you let's take somebody's example who is it shirish shirish what is your mass so Shir says the mass of shirish mass of shirish is 40 what comes to your mind 40 anything what is that 40 you need to tell me GRS kilos tons so shirish if somebody asks you your mass you won just say 40 they will think maybe shirish is 40 tons somebody else will think maybe shirish is 40 G some other person might think oh Shish is 40 quintals 40 pound 40 kilog confusion so you always need to give units yeah it could be kg or maybe he might say no my Mass is in pounds anything but you need to give something in front of it that something in front of it is basically called as the unit so if I say mass is 40 kg or if I ask height whose height shall we take whose height shall we take somia somia what is your height somia somia says sir my height is 170 sir I will be like 170 ft oh my God you are like Kar or that leaning tar of pizza orward no so then s will say no sir it was in centimeters okay fine it is in centimeters so that centimeter is the unit so guys this is nothing but your value this is nothing but your unit same thing this is nothing but the value or the magnitude also you can call it magnitude of the physical quantity and this is again the unit this is our physical quantity so in general any physical quantity is the magnitude is the magn itude or whatever you want to call it the value times the unit times the unit symbolically you will write it as physical quantity magnitude is generally symbolized by the number n n is that value that number which comes over here 40 170 unit is having the symbol U So Physical quantity is n into U this is a standard formula which you should know n into U is this absolutely clear my dear Warriors what is this formula and what does it stand for any physical quantity is magnitude times unit correct very good oh my god really Samia your height is 770 what a guess I thought it will be I just chuma guessed it my height is like 176 or something so I thought okay somewhere around only humans will be so I took a whole number very good so my prediction works every time and you will notice that as you study more from me whatever stresser predicts come in comes in the exam it happened in the mains it happened in you know even in Advan some two three questions came in J Advanced okay so anyways coming back are there physical quantities which do not have only any unit come on let's see if you guys can figure this out are there physical quantities which do not have any unit are there any physical quantities without unit without unit come on let's see if you can answer this I will be really really happy with this this is level one question this is a basic level one question come on oh visha no problem visha thank thank God this is an online class angle no angle has unit what are you guys saying saying what are you guys saying oh come on come on angle is having unit so when I say Theta is 90 degree what is a degree it's a unit or when I say Sir the angle is you know pi radian what is that radian it is also unit so it has units guys that is wrong angles have units yeah there are many things somebody saying current no no no no it is not current you will learn that there are many many quantities which do not have unit best example which everybody will know because 10th standard you have passed no everybody have passed 10th standard pakka so do you know this quantity called mu which is your refractive index refractive index yes that has no unit what is refractive index measured in I don't I can't think I can't remember nothing it does not you know it's not written in terms of any unit exactly you also might have learned of this term relative density relative density or basically specific gravity specific gravity it's the density of that object upon density of water so if I measure density of water in some unit same unit come here they will cancel and it will unitless completely unitless yes you will also see some more quantities like strain strain you will see it later on don't worry about it so where did it come from strain is basically how much is the change upon how much is the original quantity the change in the length upon the original quantity it is again unitless correct refractive index even uh you know magnification correct very good even uh you will see relative permitivity relative permeability yes density is derived even you will see coefficient of static friction kinetic friction no unit for that again so there are there are things basically you should know that there are things which do not have units okay akriti good evening join in little bit late guys yeah perfect so now when I say units think about it think about it guys if I Define the units I will come to that Meme shortly I know you guys are thinking sir what was that Meme please show me hold on if I Define the units for fundamental quantities as well as the supplementary quantities don't you think I Define the units for every single thing if I know the units for these and these because everything else is derived from this I have then got the units for every single thing so we have to know know now what are the units for every single fundamental quantity exactly so for length usually we use meter might be like sir what is a meter the definition of a meter is very complex but you don't have to know it for your J okay you don't have to bother about it so much but actually what happens is you know one meter is 1 6 5763 which is basically I think uh yes it is 16 50,7 6373 wavelength in vacuum of radiation corresponding to the transposition between the levels 2 P10 and 5 D5 of the Krypton 86 atom or the distance traveled by the Light in vacuum in 2 lak9 or sorry even more than that 299792458 second that is called as a meter that's how meter is defined for us we like sir I thought meter was just to get a scale sir you measure from here to here that is a meter but the problem is you cannot just say from here to here is one meter because what is that here to here how do you know somebody else will not measure it slightly differently so it has to be in such a way that it does not change with time with space with pressure with temperature and all of that or else everybody would say the length of Shas s's hand is 1 meter tomorrow Shas s grows old the hand becomes long everybody will go crazy the length will change I can't say the foot size is one foot exactly no that is wrong because it will change with time I will age people will age right you cannot replicate you can't carry my hand or foot everywhere and you're like okay sir we need to measure one meter sir please get your hand this is done in Laboratories this is done in proper setups to exactly measure one meter and that's how they calibrate manufacturer scales same way Mass also has been defined same way time also has been defined so there is a nice long definition of how these units come that is a separate class altoe let's not get there main thing what you should understand is whenever we Define units it should be easily reproducible it should not change with time and other external factors it should be you know constant it should not you know change because of something else so these things when they are check mark checklist is like okay okay okay that's when you can Define the unit in that particular fashion so my dear Warriors there are many other units of length by the way I don't know how many of you knew this light ear is also unit of length light year is also unit of length sir who will Define one meter very good Kari who is going to Define one meter this one meter was defined by the scientific Community not by me not by your teacher not by by your school principal not by NTA person there was a scientific committee which was formed they did lot of experiments and they're like okay every time this is not changing everywhere this is same it is constant I can reproduce it so they defin a meter a kg a second and other things okay that's a scientific Community remember that yeah one light here you know it's like crazy is a distance traveled by light in one year it's crazy I mean light travels just visualize this three lakh kilometers in 1 second your bloody car even if you buy a nice BMW or Mercedes or Audi or Lamborghini or Ferrari Porsche okay I don't want to talk about Porsche Porsche is these days okay in the news okay you talk about Lamborghini whatever sir it travels 350 kilom per hour sir per hour how many per second 50 km in 1 hour I'm telling you light travels three lakh kilometers in one second that's crazy insanely large speed and imagine that goes on for one year it goes on for one complete Year yes madum will come to errors also so that is a light here and other units are also there you should just know about it astronomical unit is the distance between Sun and Earth okay Parc is the distance which this uh you know one astronomical unit subtains an angle of one Arc or basically 1 by 360th of a degree so basically if this is the Sun and this is the Earth this is the Earth so if you are standing here this is the angle subtended if you stand little bit far away this is the angle subtended so you stand oops you stand so far away that the angle subtended is basically 1 by 3,600 3,600 of a degree that distance which is there is called as a Parc that distance which is there is called as a Parc Okay so these are this is how these things are being defined you just have to uh have a slight idea about it okay very good visha U yeah even I'm very poor in essay writing so that's why I do not buy such cars you know what I mean all right CH let's go to the next thing and let's see what are the different systems of units different parts of the world people have their own own convention right we have our own convention so most of the people around the world use mkss that means they measure length in meters that's M mass in kilogram that's that K time in second that is that s in that MKS system got it my dear Warriors mkss MKS system is what is widely used but britishers they are crazy they use foot pound and second so britishers they measure length in feet the swimming pool is 16t deep your height is 5 ft even we use it because we are ruled by British Mass is measured in pounds thankfully we don't use pounds it's crazy time is in seconds then there are another bunch of people who use CGS I don't know why so many systems chuma length is in centimeters that's the C mass in gram that g over here is that G over here time is in seconds that is that s in that CGS so CGS MKS and FPS these are the three widely used systems you can also make your own system nobody's stopping you but it will not be printed in the textbook that is the problem okay so these are the three widely accepted out of that MKS is more widely used and more natural to use why is it more natural because yeah you can have your own pandu unit because it's very simple yeah 1,000 m is 1 kilometer 1 by, of a meter is a millimeter th000 G is 1 kilogram that's how it is uh in in in fps and all it's crazy 3 feet is one yard some number of yards is you know one furong some number of fongs is some one mile it's a crazy system that's the reason why we do not use it so widely but britishers love it okay so length meter kilogram is mass time a second but the problem is these three are not the only fundamental units there are more fundamental units correct yes or no there are more fundamental units so if I extend it further the MK system for the remaining four for the remaining four uh you know fundamental quantities then the MKS plus that additional thing is called as SI system of units what is it called called SI system of units so MKS is a subset of SI system MKS is a subset of SI system so when you write it down for all the units oh sorry fundamental quantities length mass time obviously the first three apart from that current temperature light and amount so length in meters mass in kilograms time in seconds current is in ampers a is the symbol for that like seconds has s kilogram has kg meter as M temperature is in kelvin not in Celsius nor in Fahrenheit it's a new scale which is called as the Kelvin scale the symbol is K intensity of light Candela symbol is CD and amount of a substance is measured in mole m o e and you will learn that in mole concept which is m o that's a shortcut okay everyone with me hello parishad yep very good very good awesome and for the plain angle it is a radian for solid angle it is Stan it is steradian okay Sr is the symbol radian rad is the symbol for it or the shortcut way of writing it so all these things you should know the fundamental quantities in SI system what is it measured in and what is their symbol be for the original seven or the two supplementary units and you should know that SI system is a super set of the MK system MK system is only limited to length mass and time the other four quantities with the supplementary units if you involve them that becomes your SI system of units that becomes your SI system of units is this point clear everyone very good excellente excellente Perfecto Perfecto okay now remember you can also change from one unit to the other and you should know some basic conversion factors like like for example like for example uh say you talk about you talk about grams G when I write when I write K G it is basically 10 to the power 3 G that K stands for 10 to the^ 3 these are your prefixes to go from one to higher or lower unit then you also have then you also have small M into G that is milligram that is 10 to the power minus 3 10 the^ minus 3 you can also write micro G which is 10 the^ - 6 then you also have n small G which is 10 the power - 9 then you also have p g that P stands for PCO which is 10 the^ min-2 these are your prefixes you also have FG which is 10 to the power I just don't have much space but still I'll write it 10 the^ minus 15 so guys what are these things called This is basically your Millie this is basically your micro this is basically Nano this is p Co and this is basically fery or sometimes also called as fto so these are your lower units you go smaller and smaller and smaller so Millie micro Nano Pico fto -3 - 6 - 9 -2 minus 15 you can go higher these are bigger units okay or bigger prefixes after kilo comes Mega comes Mega so that is basically 10 to the^ 6 okay then you have Giga GG all these are capital symbols 10 to the power 9 then you have TG which is 10 the power 12 10 the^ 12 this is basically your kilo this is basically your mega this is basically your Giga this is basically your Tera me kilobyte megabyte gigabyte terabyte that is how it goes KB MB GB TB right hard disk sizes everybody knows this so this is how it goes everyone till this point very very clear my dear Warriors awesome so these are basically your prefixes to go below smaller units or larger units you should know all these basic basic things okay and other things also like standard conversion factors you should know like 100 cm is basically 1 M right if you go to mm instead of G if I put M millimeter it will be 10^ minus 3 m so standard things you should know even uh speed conversion formula like if I know it in kilometers per hour if I know it in kilometers per hour so 1 kilometer per hour is 5 by8 m per second 5 by8 m/ Second so some basic things you will learn as you go progress ahead okay and we'll learn more and more physical quantities so what is happening in these things is that this is a different this is a different unit this is a different unit this is a different unit so the number changes do you see the number has changed that is exactly what I'm talking about over here here the number is one the unit is U1 here the number is two the unit is U2 but the quantity is the same so N1 U1 is N2 U2 is a very very standard Rel relationship which you should know basically the numerical value might change if the unit changes if the unit changes the numerical value might change you can see that here also N1 U1 is N2 U2 the numbers are different units are different got it clear okay we'll come to dimensions parishad in a bit we have not yet talked about Dimensions first let's complete units the SI unit of momentum which is mass into velocity is think about it can you get the momentum's SI unit okay I think you can come on this is a I think it should be a level one question only or yeah momentum is mass into velocity how is mass measured Mass is measured in SI units in kg velocity is displacement by time displacement is measured in meters and time is measured in second so the momentum will be measured in kg into meter per second kg meter per second that's option number d d for it Delhi let's see if you guys have written it down very good harika farisha Gabi hanuma very good NRI hariharan very good ABD awesome aishi very good STI awesome Kumari very good VES next question on your screen next question on your screen the following two statements are given I think this is a level two question okay I'm guessing uh statement one says astronomical unit parse SEC and light here are the of measuring dist statement two says Au is less than Park is less than your lie what do you think is the correct option what do you think is the correct option okay think about it this is a statement based question we just did one slide over there and I told you just vaguely remember what it means just vaguely remember what it means then you can definitely solve it okay let's go back to that slide let's go back to that slide so that you remember what the things were astronomical unit is the distance between Sun and Earth obviously it is not going to be one light year one light year is huge the distance traveled by light in one year Light reaches the earth from the sun in 8 minutes so obviously astronomical unit will be much lesser than one light here that is so for sure Park is the distance where the angle subtended between Earth and the Sun is you know 1 by 3,000 of a degree that is 10 the^ 3 kilometers 13 km it's more than it's more than a lier it's more than a lier guys so now you know whether this is true or false whether this is true or false I think this is false obviously the park should have been the largest lier in between Au which is the astronomical unit should be the least so guys statement one is correct statement two is definitely not correct correct everybody understood this very nice option C very good very good so this was a level two question sometimes they ask you from ncrt so please read ncrt and go you cannot Skip ncrt and expect that you can solve it now any physical quantity I give you you can always find the unit of it it's not that difficult if I tell you if I tell you you know uh see there is a term called as energy density which is energy per unit volume energy per unit volume U is energy and V volume energy is nothing but energy is nothing but measured in Jewels is measured in Jews volume is nothing but measured in Meer Cube so the unit of energy density unit of energy density Jew per M Cube as simple as that you tell any physical quantity if you know the formula you can always get the unit for example the gravitational is given by G M1 M2 divided r² what is the unit of G so write down therefore G is equal to force into r² ided M1 M2 so guys now you know what should be the unit of G force is measured in Newton force is measured in Newton distance is measured in meter Mass one Mass 2 so this is kg into kg so that will become kg Square kg into kg will become kg Square so the unit of G is Newton met Square because this was R square Newton M Square per kg Square Newton M Square per kg Square got it everyone how this works if if you know the formula you can get the units if you know the formula you can get the units of any godamn physical quantity so don't have to worry now let's come to the next part of the chapter which is called dimensions and I hope you are understanding everything with the flow and I hope the speed is right and I hope you guys are you know enjoying the class too yep so let's talk about Dimensions now you take any physical quantity if it is a derived quantity I will write it in terms of the fundamental quantities when I express it in terms of those fundamental quantities maybe the powers of those fundamental quantities could be anything 1 2 3 5 min-1 min-2 when I write it in that form when I express our derived quantity as fundamental quantity with suitable powers that is called as the dimension of the physical quantity so say for example very simple example I give you very very simple Leto example volume volume is basically length into breadth into height whenever I want to express Dimensions the way to show that is by putting square brackets so when I write dimensions of volume I will put square bracket volume that means I'm interested in the dimensions of it so I will just put l into B into H dimensions of L into dimensions of B into dimensions of H what is length measured in it is measured in length only what is breadth measured in it is fundamental quantity it is measured in length only height is also measured by measuring the length between two different points so basically it is nothing but length into length into length three times so length raised to three so the dimensional formula for volume is length raised to three the dimensional formula for volume is length which is fundamental raised to three because all the three things are measured in terms of the length but writing this length every time is a very lengthy process so the short form for length is cap cap L I can put this square brackets I can put this over here if you see this over here L Cube and then square brackets it's one and the same thing don't get confused don't get scared okay this is perfectly normal you put three outside or three inside it's one and the same thing so I can say the dimensional formula for volume is L Cube the dimensional formula for volume is L Cube as simple as that so every fundamental quantity every fundamental quantity has their own symbols where is it I think I did not put it okay so let's go back over here yeah let's write down the dimensional formula over here what is the what is the dimension what is the dimension of all the fundamental quantities what is the dimension of all the fundamental quantities okay come on guys length the symbol for that is capital L the symbol for that is capital L for Mass the symbol is capital M okay Dimensions guys this is length this is mass then for time it is basically written down as capital T with square brackets to symbolize Dimension electric current is symbolized with capital a same as the one in units with square brackets thermodynamic temperature that is a temperature it is measured in kelvin and the symbol dimensionally is also capital K only intensity of light is basically Capital C Small D okay with square brackets and quantity of a substance again over here capital m o you can't use M because M has been used by mass so that's why you put M over here that's all these are the dimensional formulas of all the seven physical quantities now I want you to tell me what is the dimensional formula for the plain angle and the solid angle if you answer this this is level two question guys if you answer this I'm really proud of you really proud of you come on guys plain angle and solid angle what is the dimensional formula what should I put over here and over here what should I put over here and over here come on guys let's see if you guys can figure this out quickly in the chat box quickly in the chat box yes SAA Prasad I know the final answer key came very good samama very good aanish very good Su very good excellente uh hariharan December 2024 is too late we'll complete the entire syllabus much before that much before that yes they are dimensionless they are Dimension less so a lot of people think if something has a unit it has a dimension wrong this is the best example for that just because it has unit does not mean it has Dimension it is a completely dimensionless thing I will prove this to you what is the formula for the length of the Ark length of the Ark is radius into Theta so the dimensions of length is the dimension Dion of R into the dimension of theta so the dimension of theta is the dimension of the length of the Ark dimension of the length of the Ark upon the dimension of the radius length of the Ark is dimensionally capital L radius is also length so it is again l l l will cancel what will you get nothing over here so guys Theta is completely dimensionless quantity same thing for solid angle also same thing also okay everyone with me on this perfectly clear very good very good awesomeness so guys let's move back to our slide okay I think this we had seen before I don't know why it came over here my bad yeah so have seen the dimensions of anything now how do we calculate dimension how to find Dimensions how to find dimensions of any quantity there are two ways first way if you know the formula if you know the formula the second way if you know the units if you know the units if you know either one of this way then you can follow that method to find the dimensions of any physical quantity for example example my dear Warriors I want to know the dimensional formula for acceleration acceleration is nothing but you know velocity divided by time actually change in the velocity divided by the time right so I'll put a square bracket over here don't worry we'll learn about acceleration later on also velocity velocity is actually displacement divided by the time and this time is also here so now teally displacement is there on the top and square of the time is there below displacement is measured in length and time is measured in T So T Square so technically the dimensional formula for acceleration will be length raised to one t ra to minus 2 is there nothing else is involved nothing else is involved got it that's how you can find out the dimensional formula if you know the actual formula of that physical quantity same way over here if I know also I can find it example there is a physical quantity whose Dimensions is kg square m Cub per second what we do you will think if the UN kg s m Cub per meaning the mass dimension is having the power two so it is basically M to2 meter length length unit is cubed so the length Dimension will also be cubed time is there below so it is actually time ra to power 1 so hence the dimensions of this would be M to 2 L to 3 T to minus one which is very very easy to find very very easy to find y is this very very clear Shish only pyqs will not be completely enough I think you have to push yourself ahead just pq's is decent but I mean just to get till probably 98 99 percenti if you want to go beyond 99 percenti you have to stretch a bit further fair enough let's do some questions I think these are level one or level two questions okay so one is knowing the formula second one is knowing the units so let's see if you guys can quickly figure this out if I tell you the force is equal to 6 Pi EA r v find find okay let's do one thing let's solve it simply first find the dimensions of force first okay then find the dimensions of work okay then find the dimensions of power find the dimensions of power okay then I want you to find the dimensions of momentum dimensions of momentum okay all these things I want you to find I'll give you the hint force is mass into acceleration standard formula work is force into displacement standard formula power is work by time standard formula momentum is mass into velocity very easy to find out the dimensions now if you know this very easy if you know the formula come on my dear Warriors come on my dear Warriors I am uh over here so it's very difficult for me to go on both the channels But please understand yes okay let's start force is mass into acceleration so it is M into a and Mass is measured in capital M acceleration unit wise is meter per second square meter is length per second Square so T ra to2 that's what it is so if I write it in a very systematic form M to 1 L ra to 1 T to min-2 very good so M to 1 L to 1 T to minus 2 work work is force multiplied by displacement Force we just solved over here it was just solved over here M to L to 1 tus2 displacement is length so I have to multiply length with length so M to 1 L1 and L1 over here will make it l to 2 T to minus 2 that is the dimensional formula for work power power is work per unit time work per unit time so work is this which is basically M ra to 1 L ra to 2 tus2 whole thing divided by time which is basically T So guys this is going to be M to 1 L ra to 2 T ra to what will happen it will become T to minus 3 how many of you wrote it t to minus 3 very good GG oh it's not GG oh so sorry it was J J my God don't put it like that okay momentum is mass into velocity Mass is measured in Mass capital M velocity me/ second length per unit time so therefore M to 1 L ra to 1 T to minus1 that is the correct answer got it that's how you can find out the dimensions of any physical quantity if you know the formula similarly if you know the units also you can do it let's say for example kg inverse m/ second cub what is the dimensional formula next ampere square into Kelvin per kg squ okay what is the dimensional formula come on my dear Warriors if you know the units also you can get the dimensions if you know the units also you can get the dimensions come on yes this will be kg inverse means it is M ra to minus one meter is basically length and second is time but it is below bring it on the top it will become T ra to minus 3 time ra to negative very good here this is ampere ampere is a only a to 2 this is Kelvin is temperature so just K raed to one kg below so it is mass raised to negative power to it was there below so that's why negative power got it straightforward as simple as that very nice let's solve this next level of question which was asked in J mes okay next level okay so physical quantities and their Dimensions I'll tell you if you know the formulas you can get it easily if you know the formulas you can get it very easily so I will tell you what the formulas are I'll just duplicate this uh couple of times and I'll show you it is very straightforward so guys let me tell you Young's modulus Young's modulus is basically Force by area upon change in length by original length this is the formula for young modulus if you talk about viscosity coefficient use this force is 6 Pi EA r v therefore EA is basically Force by 6 Pi RV for this one for planks constant use energy is equal to H into F so H is basically energy by frequency for work function work function is basically Just Energy so it is just basically same as energy which is same as work same as work okay so dimensionally it is same as work because work function is just the energy required so it is dimensionally equivalent to work only now now if you know the formulas it becomes easy like sir I don't know these formulas yet that's what I'm trying to say you'll learn these formulas later on so for example for work function it is dimensionally like work it is dimensionally like work so what is the dimensions of work we just did it some time back we just did it some time back right over here M1 l s tus2 that was the dimensional formula for work right so that that's it it's just going to be it's just going to be Mass ra to 1 length ra to 2 T ra to minus 2 is it there m to 1 l s t to minus 2 yes it is there right over here it is there right over here everybody with me D is going with four same way yes it is same as energy energy work Everything E is equal to HF it is basically energy by frequency so guys energy energy is same as work energy energy is same as work frequency is one by the time is one by the time so energy is same as work means M to 1 L to 2 T to minus 2 this is 1 by T So time goes on the top what will happen you'll get M to 1 L to2 T with minus 2 will make it minus1 so T to minus1 M1 l s M1 l s t to minus one so this goes over here this goes over here work function was over here is that clear so similarly you can solve it for the others similarly you can solve it for the others like for example if you solve it for this guy force has the dimension of M1 L1 T to minus 2 6 and Pi are dimensionless R is radius which is length and velocity is length per unit time so T to minus1 so what will happen what will happen see this m to 1 uh this L and this L got cancelled one L went on the top became L ra to minus1 this minus1 and minus1 canceled so T to minus1 so M1 L to minus1 T to minus1 so this is basically this this was this this was this naturally the remaining one will be for the third one so as simple as that this was going with this this was going here this was going here so naturally this will go over here that's it as simple as that using this formula also you'll get the same thing got it how we use elimination method to solve this that's the following question okay the answers are mentioned here exactly a is going with three B is is going with one C is going with two and D went with four perfect we solved it moving on what is the use significance of Dimensions very straightforward three uses only to verify the correctness second to derive a relationship third converting units from one system to other system what it means I'll explain you in detail we use the dimensions for check corre correctness of an equation sometimes even for eliminating options you can also use it for deriving relationships and the last one is to convert from one system of unit to the other system of unit let's talk about the physical correctness first let's talk about the physical correctness first tell me is okay the dimension of length multiplied by the dimension of mass is actually M to 1 L to 1 is this correct yes or no quickly tell me yes it is what about this m to 1 L Square divided m² into is basically just like you know normal division it will be M ra to minus1 L ra to 2 T ra to minus1 so you can multiply one dimension with next Dimension you can divide a dimension with the next Dimension what about this dimension of Mass plus the dimension of mass what do you think this will be what do you think I will get over here and similarly tell me over here also dimension of length Square t to minus1 plus dimension of length Square t to minus1 minus a dimension of L Square t to minus one what do you think I'll get over here or let's just use only uh one of them that's okay what do you think I'll get over here versus here come on my dear Warriors what do you think is the answer for this dimension of a mass plus the dimension of a mass I will get dimension of mass only a lot of people think there should be two over here or probably M Square over here no when I add Mass with mass I will get Mass So dimensionally speaking I'm still getting Mass so don't put 2 m number two when I subtract this with this I'm subtracting a quantity of certain Dimensions with a quantity of same dimensions I will get a quantity of those same dimensions so it will be L ra to 2 T ra to minus1 only there is nothing wrong over here right so do not put zero a lot of people put zero sir this minus this you are treating it like variables this is not x - xal 0 or x + x = 2x no these are not variables that's what should get inside your head these are the dimensions I can add apples and apples together 10 oranges minus two oranges will be eight oranges so it is talking about the type of the quantity so the type of it what is the 10 type orange what is the two type it is orange what is remaining type it is also orange so when I put square bracket it represents the type of that quantity which is length mass time whatever but tell me this what about this length plus Mass this is wrong guys I cannot do that even this l s m minus M tus1 this is also incorrect because they are of two different types Whenever two different types are there I can't add them I can't subtract basically it is mathematically only wrong it is mathematically only wrong keep this in mind yes so whenever I have an equation whenever I have an equation and I put equal to I have the left hand side I have the right hand side now on the right hand side you might have physical quantity phys physical quantity 2 physical quantity 3 here also some physical quantity 1 physical quantity 2 physical quantity 3 Etc it's this could be added subtracted I don't know something and all is happening what should happen is the dimensions should be the same on the left hand side as well as on the right hand side such an equation is set to be dimensionally correct or dimensionally consistent consistent thing is also called as your principle of homogenity homogenity homogenity homo means similar homo means similar yes homogeneity meaning similar Dimensions only can be added or subtracted it is illegal to add or subtract dimensions of two different kinds multiplication division is perfect no problem the problem is only when it is added or subtracted uh Shish dimensionless also if one quantity is dimensionless you can add and subtract only with a dimensionless number you can't obviously add it with a number with a dimension okay it is going to work for dimensionless quantities also now how do we use this okay so I have put up a question I think it is level one question it is again not seen in the PDF which you will get you will see it okay so look at this x is equal to a t + BT squ where X is distance in kilometers T is time the units of A and B okay actually it should have been the dimensions of a and b are not the units I wanted to put units the dimensions the dimensions of a and b are see guys look at this equation look at this equation x is equal to a + BT s left hand side right hand side don't you agree if an equation is given then dimensionally it should be correct so the dimensions on the left hand side and the right hand side should be matching not just that not just that because few of the terms are being added or subtracted few of the terms are being added or basically subtracted I can also say each of these terms also have the same Dimension have the same Dimension right all of them have the same Dimension now think about it and tell me what is a dimensional formula for x what is a dimensional formula for x guys come on quickly think and tell me yes it is length so L is also a into t also length is b into t² nothing wrong over there each of these physical quantities will be equal to the dimension of length x is in distance so distance is in length exactly so now think whenever quantities are multiplied no issues division no issues Dimensions also get multiplied and divided accordingly so a into dimension of time over here so that is L therefore what is the dimensional formula of a it will be take time below L to 1 T to minus1 that's the dimensions of a similarly about B over here this is dimension of B into dimension of t² this is dimension of length so the dimensions of B are length raed to 1 T ra to minus 2 length rais to 1 T to minus 2 yes equal to the dimension of BT yes yes Shish all these three dimensions were equal all of them should have the same dimensions of length that's what I mentioned over here all these three so the dimensions of X will be the dimensions of at which is equal to the dimensions of BT Square which is the dimensions of length because they are being added or subtracted it has to be equal yeah dimension of time is T yes correct very good shall we go to the next question I think this is the level two question let's see if you guys can figure this out find the dimensional formula for Alpha and beta this is next level problem guys okay this is the next level problem let's see if you guys can figure this out I think it was some level let's see where did it go yeah this was that I think it was right over here yes level two question wow level two question Cool let's see if you guys can figure this out come on my dear Warriors in this particular equation this guy this guy and this guy added subtracted left hand side right hand side should have the same dimensions so very quickly Alpha by t² should have the same dimensions as Force into velocity should also have the same dimensions as beta by x² I think let's take it part by part if I take these two together the dimensions of alpha by the dimension of Time Square will be the dimension of force force Dimension is M to 1 L to 1 T to -2 into dimensions of velocity L to 1 T to minus1 Take Time Square on the top therefore Alpha will have the dimension of mass is not there anywhere else except for here L is there here and here so it will become l s tus2 t to +2 will cancel only this one negative power will remain so that is the dimensional formula for Alpha just looking at these two now just look at this and this and see what do you get just look at the second and the third one dimension of force is mass ra to 1 L to 1 tus2 velocity is length ra to 1 T to minus1 is the dimension of beta which I do not know upon x x is basically length so length Square so therefore beta's Dimension will be mass is there only one time so M ra to 1 L ra to 1 L to 1 L ra to2 will become L ra to 4 -1 -2 will make it minus 3 that's it that is the dimensional formula for beta we got it how many of you got it how you got it very good Anand also got it Bala wow very good ml s tus one very good so in case of dimension of force equal to Alpha equal to Velocity equal to Beta no sharish I hope you guys got it it is this whole ratio will be equal Al to force into velocity which is also equal to Beta by x² this number is added to force into velocity so ratio will have same Dimension as Force into velocity same thing over here on the left hand side cool is this clear yes take F and Alpha by T yes on one side and the other side you can find beta through Alpha ALS yes yes you can find beta through Alpha also no issues yes yep you can equate this with this because you know Alpha from here no issues you will still get the same answer okay so nikil what we just did just like in the previous problem what would we do this Dimension is this Dimension is this Dimension like I said over here this is this is this same thing over here Alpha by t² F into V and beta by x s all have the same dimensions so I took these two together Alpha t² force velocity then force velocity beta length Square you just have to take L Square here do simple maths here you just have to take Time Square on the top do simple math and you'll get the answer cool simple power analysis yes V on the uh jungle in The Jungle Book you'll get it the DPP let's go to level three ready for level three if you crack this I'm proud of you if you crack this I really really proud of you I will give you the formula don't worry about the formula don't ask me sir I don't know the formula I'll tell you the formula the formula is force is equal to 1 by 4 Pi Epsilon q1 Q2 ided r² this is what it is uh and charge is basically current multiplied by time and energy is uh basically H into uh frequency which is basically H by time okay these are the formulas whatever formulas you need for solving the question I have given so the physics part formula wise is over now you just need to use your units and dimensional analysis come on come on let's see if you guys can figure this out yes it is the answer for the uh previous question is correct no issues with that all right so let's try to think about it let's try to think about it energy is there over here energy is nothing but Force multiplied by displacement and force is over here interesting let's see if you can do something about it let's see if you can do something about it so guys observe this carefully now energy is same as work work is force into displacement force is this one which is oops force is basically 1 by 4 Pi Epsilon q1 Q2 ided r² that is the force into displacement which is s is equal to the energy is equal to the energy which is H divided by time because it is H FF frequency is one by time okay now the question is something and all is given you want to get a dimensionless quantity you want to somehow get a dimensionless quantity let's try this out what I feel over here let's take 4 Pi do you see four and Pi these are pure numbers do they have any Dimensions no right they don't have any Dimensions let's take four and Pi on the other side rest everything on this side so I will have q1 Q2 q1 Q2 / r² into s into t ided h ided h okay uh and also Epsilon KN from here is equal to 4 Pi is equal to 4 Pi now charge is current into time charge is current into time so dimensionally speaking this is current multiplied by time this is also current multiplied by time this is displacement and this is time this is r² H Epsilon is equal to 4 Pi everybody fine till this point everybody F till this point I've just written charge as current into time current into Time s is there from Before Time went on the top H came below Epsilon not and R square is there as it is now this is level three J Advanced question we have to be very careful now write down the dimensional formula of each and everything write down the dimensional formula so like for example this is current Square time time time is there three times so T ra to 3 is there uh we also have displacement over here we also have R squ over here H over here Epsilon not over here is equal to 4 Pi So dimensionally speaking dimensionally speaking dimension of current is ampere dimension of current is a so ampere rais to then time time basically uh oh can I get rid of time also somehow because time was not there over here because speed was there oh so I will get rid of it no issues this time which is there this time which is there this time which is there guys use this formula speed is distance divided by time therefore time is distance divided by speed time is distance divided by speed so I can just put over here distance is s divided by speed which is basically C so s Cube over here C Cube over here s Cube over here C Cube over here because T into T into T was basically T Cube so that t Cube I have written it down as s Cub by C Cub everybody fine why did I do that because I saw there was no time involved over there okay so now now what else is there what else is there uh yes this is done perfect okay one distance will still remain one distance will planks constant is there Epsilon not is there current is there uh yes and okay that s is there okay so let's see I think we should get over here Amper Square perfect no problem over here distance into distance distance into distance is distance raised to 4 so length raed to 4 is over here length raised to 4 is over here okay then over here R square and H R is also length R is also length Okay R is also length so I will write down length raised to two over here length rais to two over here H is as it is H is as it is I will leave it over here H is as it is I leave it over here uh oh wait a minute I didn't have to write in terms of current I'll tell you why I'll tell you why because this was e to Alpha this was e ra to Alpha e means basically the charge so I don't even have to do all these things hold on let us come back let us come back over here let us come back over here let us come back over here I don't even have to do these things I can just write this Force I can just write this particular Force as 1 by 4 Pi Epsilon charge has the same Dimension as e charge another one also has the same Dimension as e and then I have r s and then I have r² okay perfect Force into displacement is energy force into displacement is energy and energy is H BYT energy is H BYT so if I take this whole thing if I take this whole thinging and multiply by displacement so 1 by 4 Pi Epsilon charge 1 charge2 divided r² I multiply it with displacement multiply it with displacement I get energy which is planks constant divided by T which is Plank's constant divided by T okay so now I have got e over here I have Epsilon here I have head over there I just don't have C right now I just don't have C right now no issues just look at this dimensionally speaking this is e s 4 Pi is a dimensionless number Epsilon KN I will just leave it as it is dimension of s is basically length dimension of R is also length but square of it but square of it h dimensionally i just leave it as it is this is time so dimensionally this is basically T this is basically T so now this is the dimensionless quantity which I'm looking for this is the dimensionless quantity which I'm looking for so just rearrange this just rearrange this observe observe carefully observe care if I shift it on top if I shift it on the top what will I get if I shift it on the top what will I get I'll get e Square I'll get e Square as it is okay no issues what else will I get length and length square one of them will cancel only one length is remaining only one length is remaining okay only one length is remaining perfect no issues then Epsilon KN is also remaining below Epsilon KN is also remaining below okay Epsilon not is also remaining below time is coming on the top H is coming below time is coming on the top and basically H is below H is basically below this is what I get now observe this what is length by time distance by time it is basically speed so it is e Square length by Time dimensionally same as the speed and this is Epsilon KN and this is basically H so it is e to minus 2 C ra to sorry e to + 2 e to + 2 C to minus1 Epsilon ra to minus1 H ra to minus1 this is that dimensionless quantity which I was looking for so in general if I raise it n in general if I raise it to n what will happen everything will raise to n so it will become e to 2 N C to minus n Epsilon ra to- n hus I think I have got the answer E's power is 2 N C's power is basically minus n epsilon's power is minus n h power is also minus n so 2 N minus n- n minus n that is option number a option number a is the correct answer option number a was the correct answer okay why can't we directly apply the dimension formula of respectively that will be much lengthier process I see that when I write it like this four and Pi are dimensionless number so that's the reason that 4 Pi I got it over here that's the magic that we have done this dimensionless thing I got it over here this H I took it on the other side time also I took it on the other side that gives me the solution in a easier man because everything was measured in terms of these quantities is h e Epsilon finding the dimension of Epsilon H is much more task yes okay that's why it's a level three question moving on to the next type of problem where you convert one physical quantity into other physical quantity see guys if you want sorry one physical quantity in one unit to another unit I had just told you when you change the units what happens you use the formula N1 U1 is equal to N2 U2 N1 U1 is basically N2 U2 this was the guiding force this was our guiding formula but just to give you an example just to give an example to convert from one unit to another unit all you should know you should you should know the conversion factors of the fundamental of the fundamental units and the dimensional formula and the dimensional formula if you know this thing and this thing you can come from one unit to the other unit very easily you can go from any unit to the other unit in very very easy manner I'll just show this to you I want to convert 5 Newton into the CGS counterpart tell me Newton is the unit of which quantity Force so do I know the dimensional formula for force do I know the dimensional formula for force yes it is mass raised to 1 length raised to 1 T rais to minus 2 everybody with me this is the dimensional formula so you should know the D dimensional formula to convert from one unit to the other unit next thing you should know the conversion factors you should know the conversion factors I think that part I know which is from CGS to SI system one is SI units one is CGS unit so think about it I think I know this 1 kg is basically 10 the^ 3 g 1 m is 100 cm 1 second is 1 second only in CGS unit this was CGS this was SI correct this was SI system this was CGS system you should know the conversion factors of each of the individual fundamental units okay I know that now how do you convert it simple observe 5 Newton because a Newton has the dimension or Force has the diens of mass length tus2 if you write it in fundamental units what will it be a Newton will be 1 kg will be there kg ra to 1 a meter will also be there and second will be there below do you guys agree with this kg m/s square if you convert it into fundamental quantities if you write it into fundamental quantities perfect now now what is 1 kg look over here 10 to the power 3 gr okay perfect 10 to the power 3 G what is 1 M it is 100 cm what is 1 second it is 1 second only ah Perfect 10 ^ 3 into 10 ^ 2 is 10^ 5 so 5 into 10^ 5 G cm per second Square that's it that is the CGS unit and that is called as a DME in CGS the Newton is called the dime okay it is measured in terms of dime gram cimeter per second which is the CGS unit so that's it I convert the Newtons into the CGS counterpart it is that simple you just need to know two things what are the two things you need to know the dimensional formula and you need to know the individual conversion factors for the fundamental units that's all that's all as simple as that CGS is gram CM second remember that I just told you sometime back any unit any physical quantity you can convert guys for example there is a physical quantity whose Dimension is m² L by t² and let's say there is a new pandu unit and let's say there is a new pandu unit okay and in that pandu unit what happens is 1 kg is equal to 10 uh unit Mass 10 unit Mass 1 meter is let's say two uh unit length 2 unit length and 1 second is1 unit time .1 unit time so think and tell me think and tell me how much will be how much will be 10 10 okay SI units 10 SI units will be how much will be how much in the new units will be how much in the new units that is the question will be how much in the new units is the question the dimensional formula is given individ usual fundamental quantities conversion is also given to you okay let's try to do this let's try to do this first of all what will you do 10 SI units meaning first write down 10 what will be the SI unit of this physical quantity Mass raised to two that means it will be kg ra to 2 length length is measured in meters so meter ra to 1 time is there below second Square kg square meter per second square that is some new physical quantity I don't know what it is but it is some physical quantity now write down each and every single conversion factor starting off with kg 1 kg is 10 units Mass so unit Mass 10 unit mass and this is squared so this is also be squared leave it meter how much is a meter two unit length so two unit length that's it raised to whole thing divided by second 1 second is 0.1 unit time 0.1 unit time but raised to two but raised to two all right let's see what do you get let's see what do you get I can see 11 10 is there this 10 square is there into two is there .1 square is there 0.1 square is there and we have unit mass square unit length upon unit Time Square this will be come on guys one is 1 by 10 so Square will be 1 by 100 so 100 into 10^ 2 is 10^ 4 into 10 is 10^ 5 so this will become 2 into 10 the^ 5 this will be the new unit this will be the new unit that's it so 10 SI units is 2 into 10^ 5 new units that's all is that clear is that clear my dear Warriors yep yep very good very good what about SI unit what do you mean by what about SI unit SI unit is a system of units for Mass you measure in kg length you measure in meter time you measure in second so when they say that you know this is Newton it is an SI system okay so understand that Newton only will be like kg meter per second square if the reverse problem comes that's what you mean you will do the exact reverse process you'll do the exact reverse process then you will write 1 G is 10 ^ minus 3 Kg 1 cm is 10 ^ -2 m 1 second is 1 second so you'll just shift the powers over here then you'll write one g is how much one cm is how much and then solve the problem that's all okay clear Perfecto Perfecto yes let's move on let's move on to the next next question test dimensionally if this formula is correct or wrong and force is f x is distance T is time so this is checking your dimensional consistency I think is a level one or two problem so check this out my dear Warriors is this dimensionally correct or wrong we have to check the consistency 2 and Pi dimensionless number okay let's go with the rhs and LS so LHS LHS Dimensions will be the dimensions of time so it should be just capital T let's talk about the rhs the dimensions of rhes will be the dimensions of 2 pi into into the dimensions of mass by force uh and divided by length the whole raised to half 2 pi is a completely dimensionless number forget about it m is M only forget this is raised to half or I just put a common power so it is capital m x will go on the top it will become length force force is basically M ra to 1 L ra to 1 T to minus 2 okay the whole thing raised to half so this will become so this will become mm cancels LL cancels T ra to minus 2 so it goes on the top it will become T ra to 2 raised to half which is just T oh wait a which is the same as dimensions of LHS so this is a dimensionally correct equation nothing wrong with it this is a dimensionally correct equation got it did my dear Warriors everybody with me clear awesome so this is how you check the dimensional consistency of any equation by matching the dimensions or starting from one side and see whether it matches with the other side you soled many questions like this now next question this is a level two question a density of a material in SI system is 128 in some new unit where length is 25 cm and mass is 50 g the numerical value of density is how much okay what did I tell you to convert from one unit to the other unit what should you know the converion factor of fundamental quantities second thing the dimensional formula these are the two things which we should know who do you have to convert density so quickly think and tell me what is the dimensional formula for density because it will be the diens of mass divided by the dimensions of volume so technically it is M to 1 L to-3 that's the dimensional formula for density first thing done next thing that I will need is individual conversion factors individual conversion factors so think about it length is 25 cm in a certain unit where the unit of length is 25 C CM 1 unit length one unit length is 25 cm but I don't want centimeter this was in kg and meters SI system so I need to do that conversion also 25 cm is 1/4 of a meter 1/4 of a meter so if I take four on the other side what will I get four unit length 4 unit length is 1 M that is the first thing that I get I take four on the four unit length is 1 M got the conversion factor till this point everything clear next unit of mass is 50 g one unit mass is basically 50 g 50 g 50 g is basically 50 into 10^ 3 Kg I want kg so I will shift it on the other side but before doing that 5 10^ - 2 K shift it on the other side so 1 kg take it over there 10 the^ min-2 will become 10 the^ 2 and that five on the top will come below unit mass unit Mass 10 the^ 2 100 100 divided 5 is 20 so 20 20 unit Mass 20 unit mass is basically 1 kg till this point is it till this point is it clear very good awesome now just do the final problem 128 kg per Meer Cube 128 kgs per Meer Cube I should know the dimensions only then I can get it I can get the conversion factor so 128 as it is 1 kg 1 kg is 20 unit Mass 20 unit Mass yes divided by meter a meter is 4 unit length 4 unit length but I have to cube it but I have to cube it come on what is 4 Cube 4 4 is are 16 16 4 are 64 128 divided 64 is 2 2 into 20 is 40 so it will be 40 unit mass per unit length Cube which is basically the new units 40 new units faulty in the new units so where is it option number a that's it that's how you solve the question is this clear is this clear Shish you will learn which are the dimensionless quantities as you progress in time in physics like coefficient of friction refractive index strain relative density all these are dimensionless quantities okay to and any numbers like 2 pi e log all these are like dimensionist s cos tan these are like dimensionless okay these are all Dimensions yeah logarithm sign trigonometric functions they are all dimensionless cool the second application so what were the two things that we learned in Dimensions till now we learned that you can basically verify the correctness of any physical quantity we saw how you can get the dimensions of any thing and match it and find it out also we saw that you can convert from one unit to the other unit very easily now comes the third part yeah we'll take a break after this we'll take a break after this third part and then we'll directly go to significant figures rounding off and all those things okay don't worry all right derive a relationship now this is the most uh asked type of question so pay attention and then we'll take a break very quickly observe see in physics if I tell you you know the speed depends on the time the distance the force and all of that then you will think that okay maybe using some loss I will get a formula for okay speed is is force into time divided by mass into acceleration something but for that you need to apply physics right you need to apply some laws some principles some theorems Etc but without theorems without physics can you get a formula the answer is yes because of Dimensions just because of Dimensions you can derive a relation between physical quantities in some cases not every time so that method I will teach you that method I will teach you the method is as follows you should know the physical quantity depends on depends on which other physical quantities other physical quantities also if there is a constant if there is a constant is a dimensionless or having or having some Dimensions or having some Dimensions this is another thing which you should know also you cannot use this method don't use this method if number one there is some addition or subtraction in the formula second if there is logarithm or there is some trigonometric function or E to something exponents then also you cannot use it what do I mean by this for example s is equal to UT + half a² I cannot use this method I cannot use this method whatever I will teach you to find the formula because there is a plus sign this plus sign is the problem this plus sign is the problematic thing over here even as simple as V is U plus a also I cannot derive V is u+ a also I cannot derive reason being this plus sign I cannot do it you will see later on there are some exponential functions formulas which you will learn later like for example or even trigonometric based X is equal to a sin Omega T you cannot use it only because of this trigonometric function over here yeah again you will learn something called as loudness is 10 log I ided I not you cannot use it again because of this logarithmic function so these are the places where you cannot use the method which I'm going to teach you but where you can use is also very interesting like for example f is equal to G M1 m / r² use it because there is no plus minus trigonometry log exponents nothing I can definitely definitely use this also I can use it for let's say uh you know some other formula also uh like like say for example uh force is equal to 6 pi EA into V some formula it is there in viscosity here also I can use because everything is multiplied or divided no issues at all no issues at all I can use it in both these cases now what is different in these two is this part over here is the constant dimensionless or having dims is the constant of proportionality force is proportional to proportional to another Mass inversely proportional to R do you see very clearly this G has some Dimensions whereas the constant over here 6 Pi it is completely dimensionless so you should know that from before only or else you cannot solve the problem or else you cannot solve the problem if the constants are there can we use it yes you can use it but you should know either the dimensions or you should know that it is R dimensionless either you know it is dimensionless or you know what is the dimension only then you can use this method is this clear okay yes why can't you use it for these things because logarithm and trigonometry is because these are dimensionless entities so it's very difficult to predict whether there will be a log or exponent how do I know okay so you cannot guess how many terms are there how many logs s cos are there okay this method simply cannot predict that okay so let's try and use it okay uh for a question I will show it to you the procedure of this and after that you will get a hang of it okay let's try it out let's try it out everybody everybody let's try it out Paka okay let's try it out let's say for example let's say for example I just tell you I just tell you listen the ball if it is dropped from the top by the time it reaches the ground the time taken the time taken to fall the time taken to fall depends depends on let's say the mass maybe the height maybe the height and uh maybe the acceleration due to gravity these are the three things can you now find the formula using dimensional analysis for the time taken for the ball to fall let's try this out everyone shall we okay what is the first thing that you will do in any kind of question where you have to derive formula is assume always start with this word assume assume the time taken is some dimensionless constant into Mass raised to some number which I don't know height raised to some number which I don't know gravitational acceleration raised to some number which I don't know I want to find x y and Zed something raised to X something raised to Y something raised to zed I do not know what those things are just assume just assume okay now any formula which you write with equal to the dimensions on the left hand side and right hand side should match yes or no the dimensions should match right on both the sides so can I then say can I then say the dimensional formula for T dimensional formula for C it is dimensionless is dimensional formula for M ra to X dimensional form fora for H raised to Y dimensional formula for G raised to Z obviously this has to be true left hand side and right hand side Dimension should match undoubtedly okay what is the dimension of time T okay but what about mass and other things I don't think it is there Mass raised to zero length is also raised to zero only time is there here mass is there one time height okay height is basically your length dimensionally so raised to Y and G acceleration meters per second Square so length ra to 1 T ra to minus 2 whole thing raised to Z whole thing raised to Z so technically this is technically this is M ra to X length is there here also here also length rais to y+ Z and time is there only once so Min - 2 Z so on the left hand side also same thing M to 0 L to 0 t to 1 understand I wrote it because on this side there was no mass or length so that's why M ra to 0 L ra to 0 anything raised to 0 is one why did I write it like this so that I can compare the powers if m is raised to Z over here M has to be raised to Z on the right hand side or else it will not match it dimensionally agree or disagree agree or disagree so dimensionally it has to match so if you check M over here and M over here 100% 0 is equal to X 100% X is nothing but zero next let's check the next number length or maybe even the time time over here and the time over here check it out T's power is one on the right hand side it is minus 2 Z so what is Zed guys it is negative half negative half everyone with me awesome last one last one over here length power here and over here L's power is zero so on the right hand side also the total power should be zero but wait a minute Z is negative half and Y is minus Z so it should be minus of minus half so what is y it is basically plus half what is y it is is + half perfect so I found the unknowns x y and Zed so I will substitute it back over here I will just substitute it back over here just see what will I get T is equal to constant constant into Mass raised to x x is0 so M ra to 0 then you have length length raised to or sorry it was height my bad height raised to what is height raised to height is raised to half which is y it is basically y so it is basically half and acceleration due to gravity acceleration due to gravity G is rais to Z which is basically minus half anything raised to zero is basically one this is root of H this is 1 by root of G so actually it will be cunk H by G that is your time so it is C root H by G as simple as that you can't find out the constant unless you do it experimentally so if you're wondering sir what to do with this C this has to be found has to be found via experiments or via laws of physics via laws of physics but you leave the answer over here okay that's it your options will be all Alo in this form only answers will be also in this form only okay understood so mass is not coming only Shish mass is not there only in the answer if some option contains Mass you'll first of all cross it out eliminate it out Mass just came out to be independent okay this is how you solve the questions let's try out one more question guys let's try out one more question everybody with me like of the chat box I know you guys want a break now after this you're going to get a break but this is the last question before we you know disperse for the break and then again return back for significant figures and errors part all right all right let's do this let's do this okay say for example the force depends on depends on density area and velocity find the formula using dimensional analysis okay let's start what should be the first step I'll give you the hint always the first step is if you know what it depends on assume first thing is assume so let's assume our force is some constant into density raed to X area raed to y and velocity raised to Z Now start substituting the dimensions of each of the following Force M to 1 Mass acceleration is L to 1 tus2 constant is dimensionless density M to 1 L to minus 3 mass per unit volume area this is A's area it is length Square length into breadth is area so length Square raised to Y velocity length per unit time the whole thing raised to Z I think let's Club all the similar things together it will be much easier so Mass raised to 1 L ra to 1 T to minus 2 is mass raised to X Mass raised to X length raed to -3x + 2 y + Z - 3x 2 Y and Zed time is only there one time so raised to minus Z that's the most condensed form that you can think of now let's try and solve it just like before I think mass is very easy to analyze left hand side R rhs the dimension should match for every single thing so one will be X or rather X will be one the next Dimension that will be matching I think is of time it's better you can see it's very easy to calculate it so Min -2 over here and minus Z over there therefore Z is equal to 2 that is also done last one length length oh my God such a big thing lens power is 1 here it is - 3x + 2 y + z wait a minute x value is 1 so it is -3 into 1 y value I don't know okay Z value is okay just put it over here -3 + 2 -1 bring that minus one over here it will become 1 + 1 is equal to 2 y or 2 Y is 2 or Y is basically one so perfect I got y x and Zed all the three things so therefore therefore substituting it back over here what should I get force is equal to con into density ra to x x is basically 1 area rais to Y which is area ra to 1 velocity ra to zed which is basically two therefore force is some constant into row a v² that is the answer row a into V sare into some constant 1 one2 got it everyone this is how you derive any formula did you get some confidence did you get some confidence my dear Warriors now yep so what and all have you learned till now what is unit what is dimension the uses of dimensions three uses converting checking if LHS is rhs consistency third thing is deriving a formula seven fundamental quantities to supplementary quantities supplementary quantities are dimensionless everything else has dimensions derived quantities are dependent on fundamental quantities multiple systems are there you should know how to go from one system to the other if you know Dimensions if you know formula you can find out the dimensions very easily that's all we have done till now let's take a quick break and we will return let's take a quick break and we'll return for significant figures okay so I'll just put a timer maybe over here 20 minutes break guys okay meanwhile smash the like button okay in case you have forgotten to do that e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e the break of time is over my dear Lions welcome back welcome back welcome back I hope you guys are all done with your dinner hopefully at least I am done and if you're not done I mean you can still watch the lecture while having your dinner and just wind it up in the next couple of minutes quickly get everybody on the channel yes let's begin let's begin with the lecture my dear Lions welcome welcome welcome welcome welcome back so before the break we have seen what units are what your physical quantity is and how they are classified into you know derived and fundamental quantities seven fundamental and two extra supplementary units those units do not have Dimensions other things have their basic dimensions and we saw how to find the dimensions and how to put it to use in three different ways uh one was to convert units one was to check the consistency of LHS rhs the last one was to derive the formula now let's go to errors part that is the last part of this chapter let's roll all the warrior pandu whistle pooing let's begin with the class where is my pen yeah it is right over here now to go to errors we need to learn this small thing which is called a significant figures significant figures and rounding off if you understand it then uh you know those error questions also become much easier significant figures means basically your digits of importance your digits of importance digits of basically importance like when I say when I say 0 07 Bond James Bond right 0 07 those zeros are insignificant I mean why do you even bother writing it this and this is completely insignificant only this is a digit of importance so the number of significant figures is just one it has one significant digit that's how we say it so my dear Warriors my dear LS there are simple rules for predicting how many significant figures are there and the rules I have put it up over here okay now these rules look like crazy easy right but let me explain this to you by simple examples okay let's have a look whenever any number is given and you want to find how many significant figures are there use these rules do not by heart understand it understand it you will not byard because if you byard you will like what is the four point what no don't do that understand it you will get it all the nonzeros are significant kind of makes sense and any two nonzeros uh are there and between that if there are zeros those also become significant so let's take an example one 9 8 7 4 5 all these are non-zero digits 1 2 3 4 5 6 six nonzero digits that's why it has six significant figures or six significant digits similarly if there are zeros but that zero is between two significant numbers like one and 8 are significant they are important digits that zero also becomes automatically important even these two zeros whether decimal is there not there does not matter between eight and nine we have two zeros so 1 2 3 4 5 6 7 it has seven significant digits so all the zeros between two significant digits automatically become significant simple rule that is the second rule so you can probably make more examples like this if I have 707 this this this important so it has three significant figures uh 5 0 0 6 0 7 1 2 3 4 5 6 this has six significant digits as simple as that whether decimal is there not there does not matter 2 0 04 1 2 3 4 that's it four significant figures that's how you count the number of significant figures moving on to the next one all the zeros that are on the right of a decimal point and also to the left of the nonzero digit this is the decimal point to the right of it and to the left of the nonzero digit left of the non-zero digit they are never ever significant so don't even bother counting them don't bother counting them so all these zeros are not significant so 7even 9 and 8 only are there as significant digits that is basically three to take an example 0.02 this zero is not of any importance it's on the left of this two and to the right of this decimal all these zeros become insignificant only one significant digit what about this 0.0 5 0 6 these zeros become insignificant because they are to the left of this nonzero and after the decimal so guys forget all these things five and six are significant and these two zeros they become significant because they are between two nonzeros so this has four significant figures this has four significant figures understood guys everyone all the lines yep yeah okay moving on to the next one coming up on your screen okay this is also done now the next rule all the zeros on the right of a decimal are only significant so when you are going after the decimal they become significant only if only if only if a nonzero digit does not follow them only if a nonzero digit basically does not follow them all right so you know you will see that all these decimals there is a zero zero like this there is a nonzero number after it no so all these zeros automatically become significant basically if I say um 5.0 this zero is not followed by any non zero it's basically after the decimal there is nothing after it automatically it becomes significant when there is nothing after it automatically it becomes significant assuming it is after the decimal assuming it is after the decimal same way this this is having two decimal sorry two significant figures same way if I write 2 0 2 0 0 0 0 first of all this two is significant this two is significant this zero is between two nonzeros significant these zeros are after the decimal and nothing is there after it automatically they become significant and so does this zero because it is again between two significant numbers 1 2 3 4 5 6 7 so this has seven significant figures understood my dear Warriors yep understood my dear Lions very very straightforward let's take more examples 5 0.0 this zero is after the decimal nothing after it definitely significant this is also significant any zeros between two significants are also significant so this has four significant figures that is your next rule okay which has been mentioned over here now all the zeros that are on the right of the last nonzero and after the decimal point are also significant I think this also we indirectly did it okay so imagine this imagine this uh something like this 0.02 0 0 the moment these zeros are after the decimal they automatically should be considered as significant but these zeros are not significant I have told this to you before also these zeros on the left hand side are not significant so this has three significant figures this has three significant figures take more examples if I take 0 0 0 7 0 7 0 this and this and this are not significant because they are on the left side of the first nonzero number seven and seven are significant this zero is in between them and this zero is after the decimal it has to be significant 1 2 3 4 this has four significant figures this has four significant figures that is is you know they're without the decimal is they without the decimal then it is basically not significant all the zeros that are on the right of the last non-zero digit are significant if they come from a measurement for example one 9 0 okay that rule is completely different but if there is meter return in front of it then this zero becomes a significant if there is no meter word here there is no decimal in between then this zero becomes insignificant so let me show this to you with an example if I write 20 M this two and this zero both are significant so this has two significant figures but if I just write down number 20 with many units only this is significant this is not significant in fact this is as good as saying 2 into 10 the^ 1 in fact powers of 10 are also not significant so this has only one significant figure this has only one significant figure to give you more examples if I write 5 5 uh 0 0 all right without any units this this and this are significant these two are not this is this is as good as saying 505 into 10^ 2 ignore this this has only three significant figures only three significant figures but if I write 5 5 0 uh kg then 1 2 3 4 5 this has five significant figures because there is a unit mentioned so whenever there is a unit mentioned Whenever there is a unit mentioned basically it's a part of a measurement then it will be considered as significant understood my dear Warriors my dear Lions is this absolutely clear what are the rules of significant figures shall we now do some questions based out of this shall we now do some questions based out of this come on I want everybody to answer this how many significant figures are there in 7 0070 how many significant figures are there in 0.070 7 how many significant figures are there in 0.077 0 how many significant figures are there in 7.07 how many significant figures are there in 70.0 how many significant figures are there in 70 into 10^ - 5 okay come on try to solve these questions my dear students my dear Lions figure these answers out figure these answers out quickly all these answers out I will write more examples also for all of you okay come on first answer very very straightforward seven and seven significant zero in between them this zero without any units not significant so it has four significant figures four significant figures for the first one very nice this seven and this seven are sign ific this zero is in between them perfectly fine this zero is to the left side of the first nonzero number not significant anything before that also not important so this has three significant figures very good many of you are getting it right now this seven and this seven are significant and what about these two zeros they are after the decimal point so they are significant but the leftand side ones are not significant so this has four significant figures this has four significant figures very good many of you are getting it right this seven this seven and this zero all three are significant this zero is in between the Sev whenever you have a decimal and then two zeros they have to be counted as significant figures keep that in mind so 7 0 0 0 Perfect all of them have four significant figures perfect okay any zero after the decimal okay and there is nothing following it it is to be counted the powers of 10 are never counted this zero is also not counted because there is no unit mentioned only one number is there so it has one significant digit exactly one significant digit da I will come live after sometime on the N English Channel let me complete this video or else it will be like halfhearted lecture then okay how about this point 7708 into 10 ^ - 5 0 0 8 0 8 0 uh 0.050 02 0 into 10 the power 3 7 okay and then 7 0 8 0 um meters okay come on let's figure this out what are the significant figures in each one of them let's start with the first one 778 and this zero is in between powers of 10 never significant any zero before the decimals not to be counted as significant so I think this has four significant figures how many of you root four very good proud of all of you any zeros before are never counted uh this eight and this eight counted zero is in between so definitely count the last zero is not followed with a measurement value so it is not significant so I think it has only three significant figures proud of you some of you said four guys be careful there is no decimal here number two it's not measured as meters kilometers nothing so do not count the last zero be careful it is not to be counted yeah okay you guys made a mistakes most of you made a mistake five obviously is significant two is significant powers of 10 never significant these two zeros are in between so counted zeros to the left uh of the first nonzero never ever counted okay this zero is after the decimal so you should count it 1 2 3 4 5 so five significant figures just check this out five significant figures exactly next one what about this what about this my dear Warriors when I put seven Dot how many significant figures are there it is basically one significant figure yes it is only one significant figure when there is a decimal and there is no zero that's it it is one significant figure if I put 7.0 7.0 then it has two significant figures this has two significant figures okay got it perfect so with just a decimal one significant figure okay not to be counted that zero is not there okay okay what about this this this and this counted there is some unit this is a part of a measurement so this becomes significant so this has four significant figures Perfecto Perfecto awesome now you are fully confident my dear Warriors my dear Lions how to count the significant figures now let me tell you you can also combine them and before you combine them you should also know how to round them off it is not that difficult see this is also going to be important particularly for all of you so you should know the rules of rounding off rounding off very very straightforward if I have 27.3 and I want to round it off to two significant figures I want to get rid of the decimal or let's say it is uh 2 73 I want to round it off to two significant figures so when I round off what you should always do is always check the last digit always check the last digit and see whether it is more than five or less than five or equal to five this number three is obviously less than the number five if it is less than number five the previous digit write it down as it is do not change anything over there so this will be just basically 2.7 that's it don't do anything to it it will just be 2.7 next let let's say for example it so happens you know the number that you are rounding of is 2.78 now you want to round it off to one decimal or basically two significant figures always check the last digit always check the last digit okay the last digit it is more than five the moment it is more than five the previous digit add one to it add one to it and write it down so my dear Warriors Lions what will it be it will be 2 instead of seven it will be basically 8 7 + 1 is 8 understood yes 78 is closer to 80 obviously and 73 is closer to 70 that zero is missing but visualize it simple but what if it is what if it is 2.75 now check the last digit the last digit happens to be equal to five then check the previous number the previous number is odd because the previous digit is odd you will add one to it and then write it down so the final answer will be 2.8 2.8 if it is equal to five and let's say by chance if it was 2.45 and now you check the last digit you check the last digit it is also equal to five but the previous digit if it is even then you don't do anything to it you keep it as even always even is favored as compared to odd odd is odd so you ignore it you always try to keep even so four remains as four so it will be 2.4 so whenever it is ending with five you have two options on both sides so the one which is even will be the correct one the one which is going to make it even will be the correct one got it as simple as that let's see if you guys can solve this particular question 2 point or let's say 26 um 4705 write it down to two decimal places two sorry not two decimal places one decimal place round it off to one decimal place so now you have to get rid of seven also and five also what will you do which digits will you check always guys guys see understand the logic here I wanted to get rid of one digit so I checked the last digit and compared it with five less than five more than five equal to five here I want to get rid of two digits because I want only one decimal place so if I want to get rid of two digits if I want to get rid of seven also and five also you have to not check the last last digit but the last two digits which which has to be eliminated but this number don't compare it with five you will now compare it with 50 is this more than 50 less than 50 or equal to 50 100% it is more than 50 if it is more then the previous number what will you do you add one to it just like if it was more the previous digit you add one to it that's it you write it down your answer will be 26.5 that is the answer 26.5 got it simple easy peasy let's try out one more number okay let's take something else like 900 or 98 uh 2 5 0 0 I want to convert it into only one decimal place only single decimal place meaning I want to get rid of this this as well as this three things I want to get rid of three things I want to get rid of so now you will check the last three digits but this time don't compare it with five not even 50 in fact with 500 oh wait a minute it is exactly equal to 500 it's exactly equal to to 500 so what will you do check the previous digit two wait a minute it is even so you don't even have to do anything you don't even have to do anything if it is equal and the previous one is even as it is if it is odd add one to it so my dear Warriors it will be just 98.2 98.2 isn't it simple understood the logic behind the rounding off everyone rules are clear how to apply the rounding off very good now that you know how to round off numbers sometimes you might need it so let's come back to significant figures and let's see how do we add and subtract numbers very simple things but you know I think uh yeah let's let's do it over here how do we add and subtract the first thing is addition and subtraction this is the first thing that we'll learn the second thing that we will learn is basically multiplication and division that is what we're going to learn addition subtraction separate multiplication division separate so let me tell you how this works very simple rules if I have the number 20. plus 5.0 versus let's say 7. minus 2. okay let's try out this addition and subtraction in case of addition or subtraction what you need to do is always the final answer will have as many decimal places as the least of the decimal places The Final Answer the final answer will have the least of decimal places least of the decimal places yes let me explain check this out 20 + 5 numerically numerically the answer should be 25 forget about the decimals 7 minus 2 numerically the answer should be five forget the decimals for now now use this rule least of the decimal place do you see over here over here there is one decimal place here 1 2 3 so this is having the least decimal place hence the answer will be 25.0 25.0 only one decimal place very good here if you notice there are two decimal and here there are three decimals so this is the least decimal place hence our final answer will also have two two decimal places as simple as that got it so easy peasy lem squeezy sir but in before question you change it to 26.5 why you won't just keep it as 26.4 which one this one uh because the previous uh in the previous question this 75 was more than 50 if it is more than what do you do if it is more more than what do you do the previous one you add one to it because 78 is closer to 80 right same way thing 475 is closer to 500 475 is closer to 500 so that's why I will write it as5 that's why I add one to it cool easy all right what about multiplication and division let's try that also it's very straightforward my dear students I mean look at this if it is 7 all right 7.0 multiplied by 2.0 okay 0 0 or let's say 02 okay 02 now if I want to multiply them and then again let's take some another number like 4 Al t. divided by divided by pi0 okay let's try this out whenever you have multiplication and division then the rule is very similar but slightly different it's not least of the decimal place it's actually least of the significant figures least of the significant figures let's try this out 7.00 and 0.02 if you normally multiply what should you get the answer as value wise let's write a rough estimate let's write a rough estimate 7 2 are 14 7 2 are 14 and this is 02 so there be a decimal place here just keep it on the Rough Side 40 divided 5 numerically should be 8 decimal places I will figure it out now let's check the significant figures 7 0 0 decimal is there so three significant 0.02 this is not significant this is also not significant so only two is significant so one significant figure exactly one significant figure is there everyone understanding this here 1 2 3 four so four significant figures this and this two significant figures who is is the least this one is the least this is basically the least in this case in this case this is the least so the final answer should also have the least significant figures eight is one significant figure we need one more so why not write it as 8.0 now this has two significant fig which is the least of them hence the correct answer for this question is 8.0 not because of the de because of the significant figure got it okay the weightage of the chapter PKA guarantee one question uh most likely two questions so four marks to eight marks out of 25 questions I mean two questions is a big deal only no okay how about this I want one one significant figure how do I write 0.14 as one significant figure guys than think about it. 14.14 is nothing but is nothing but 1.4 into 10 the^ minus1 oh this is not significant but this has two significant figures I have no other option but to round it off I have to round it off guys no other option is there with me so check this number check this number definitely it is less than five so the previous so the previous or you can even do this if you don't like it like this you can also write it as 14 into 10 ^ minus 2 so now check this number four this is less than five so the previous one comes down as it is so my dear Warriors what will happen it will be one okay it will be just one and if I put a zero no harm in that into 10^ - 2 that's the rounded off that's the rounded off value 14 is close to 10 round of 14 to the nearest multiples of 10 it is basically 10 so 10 into 10^ minus 2 is the answer remember this zero is not significant this is not significant this is significant so this has one significant figure so the answer of 7 into 02 is not 0.14 it is 10 into 10^ minus 2 isn't it crazy isn't it crazy guys yeah what a miraculous problem and this is the problem where many students will make a mistaken okay because they will think the answer should be 0.14 but the answer will be something else only the answer will be something else okay so 10 into 10^ minus 2 you can also write it as Point uh you know one that's also fine 01 is also fine yeah yes D I'll continue these classes daily only if you show interest if you don't show interest then I will be like okay you guys are only not interested so it's your responsibility morally ethically everything that you have to make this channel popular this series popular invite your friends recommend this share like subscribe put it on the status we grow as a community and it helps everyone right yeah the dpps will be Pro provided very soon don't worry after the class is over just give me some time it will be posted all right so let's find out the answers with the correct significant figures everybody try this out 98.9 plus1 0 come on try this out try out the answer next 2.5 0 multiplied by 0 0 five how much is this try this out yes 1 1.1 1 minus 1.1 1 0 no 0 and then 0 0 0 yes what is the answer for this three questions in front of you come on yes I know you guys will be regular and you want the syllabus to be completed soon in fact let me tell you I want as many lectures as possible at least 80% syllabus to be done by August or July let's let's target it let's try to cover up as many classes as many lectures as much syllabus as possible by July August you know let's target it I mean targeting is a good thing I'm not saying I will do it if I do it very good so always set very high targets uh but achievable targets so you know 100% of the syllabus if you can do it by September that will be the best thing I mean you will get September and October November December for revision so we can have October November December 3 months at least bare minimum for revision okay so let's try this out my dear Warriors my dear Lions okay so let's try this out normally if I do it without thinking about the rules this will just become this forget the zero 9 + 1 is 10 so one Carri is over so 9 and then 9 over here okay then this decimal we'll think about it 2 2.5 into .5 okay so this is as good as saying 2.5 multiplied by 5 into 10^ minus 3 which is as good as saying 7.5 into powerus 3 just leave it as it is I have not yet attached the proper significant figures so this one one cancels this one will also cancel so I think it should become 10.0 I don't know whether decimals are matching or not the answer is 10 okay now comes the thing about decimals and all those things here always check the decimals 1 1 2 so this is the least decimal here 1 2 3 1 2 3 4 5 so three decimals so this this is the least of the decimal addition subtraction means decimal places so let's write down the final answer so I should have one decimal place only so I think the answer should be 99.0 yes that is the correct answer perfect here I should have three decimal places okay so 10. yep three decimal places perfect perfect here check this out we need to check the significant figures 1 2 3 so three significant here only one so Final Answer should also have one significant figure 7.5 what will I round it off8 or seven eight will make it even so yep the answer should be 8 into 10 ^ minus 3 because that has one significant figure 7.5 has two significant figures s and five it has one significant figure why did I not write it as seven because seven is an odd number right so seven is a odd number I will add one to it to make it even cool understood clear my allons everyone very nice very nice oh why did I write 25 into 5 what am I doing guys I thought 25 into 3 sometimes it happens brain fused sorry guys why did I write it as like this I mentally thought 253 is are 75 it is 25 f are what is wrong with me happens sometimes yeah so it should be 12.5 it's 125 yeah so 10 the^ minus 3 but still I have to convert it into one decimal place so to convert it into sorry one significant figure 12.5 one significant figure that's 10 into 10 ^ minus 3 perfect so this is basically 10 the^ -2 1 into 10 ^ -2 that is the Answer 1 into 10 ^ -2 is the answer you will round it of because 12.5 no it has three significant figures I want one significant figure so 1 into 10^ minus 2 that's it oh don't put 13 13 has two significant figures Tes 13 has two significant figures be careful yeah don't put 12.5 as 13 why 13 is 1 and three two figures so what is the nearest number to 12.5 10 10 is the closest multiple of uh 10 to 12.5 got it not 20 is that understood clear everyone these confusions happen very very often in these significant figure questions let's go to the next level two level two question this is level two question let's see if you guys can solve this I feel very easily you'll be able to solve it the edge of a cube is 7.23 what is the volume with correct significant figures yes SAA even on school days we'll be taking the class at 5:00 only the reason being you can see my lectures go on for a long time so I want to be done at a decent time so you get time in the night for self-study okay so my dear Warriors my dear lions this is 7.23 multiplied by 7203 7.2 03 is the volume and when you multiply you always count the significant figures 1 2 3 4 1 2 3 4 1 2 3 4 so all of them have four so the least is also four so the final answer whatever it is whatever it is should have 1 2 3 four S significant digits only you don't even have to sit and multiply just check this this has four this has 1 2 3 4 5 six this has 1 2 3 4 5 this has three you don't even have to solve it the answer must be 37 3.7 that's it let's check it out yes answer is C understood how to solve this level two question you don't even have to do the multiplication a lot of people are going to waste a lot of time multiplying it you don't have to actually you don't have to correct very nice let's move now to the last part Supra did I ask anything wrong what did you ask where is your question I can't see your question okay error spot let me tell you there is nothing in this word which is error free the biggest I told to you as kids was if you measure something that is perfect in school tell me one thing when you are asked to when you are in second or third and you learn to use the scale the protractor right the compass and all these things for the first time and you buy the geometrical box for the first time probably one of the uh you know most exciting times of your life something new has come into your life this is a new Compass geometrical box usually you carry your pencil box so you know you measure the length of some object over here and then you use your regular scale and then you place your zero over here markings let's say this is seven and this is zero and then you're like oh sir the answer is the length is 7 mm but let me tell you no matter what you do you will have some error in that seven also because if you zoom onto it these scales these scales have markings on it so there is a room for error there is a room for error exactly there is a room for error in the measurement correct so you will see whatever measurement you do whatever measurement you do so any [Music] measurement has a scope of error in it so any measured value any measured value is going to always look something like this most probable value plus or minus plus or minus the uncertainty uncertainty in the measurement sometimes also called as the absolute absolute error in the reading so for example if I measure the length using a scale maybe the length could be 7 mm plus or minus 1 mm meaning there is a range of values there is a range of values starting from 6 mm to 8 mm the answer will be somewhere in between of this I don't know actual value if it is 6.5 6.8 7.2 7 7.99 6.01 I don't know it could be anywhere between this there is a there is a scope of you know some certainty yep is this clear what is the meaning of error and why it comes now this error can come because of many many many many reasons one of the reason is the instrument one of the reason is basically the instrument another reason could be it is completely random it is completely random suddenly the wind started blowing something fell on it so so it Bend so the instrument got spoiled and that is why you got an error sometimes the errors are basically you know completely human in nature human in nature you know one person at you know at some time he will get some other value other person the way in which they are conducting so you know it could give you a completely different value basically the human conducting it or the experiment being conducted is different so there are many many reasons why you might get different values and there is a scope of uncertainty you can never be sure what the actual value is if somebody tomorrow as an engineer you get you know what is the actual length you will never ever be able to tell it no matter how accurate your devices it will always always have a room for error is this entering your head is this entering your head T I'm very good I'm very good okay yeah aishi this is the last part of the class yep order of the magnitude that kilog Mega Giga I have taught at the beginning just check the starting part of the class everyone till this point it is clear okay now just imagine this just imagine this one pandu is is there one pandu is there and he measures the length of something length of something to be you know 10 M plus or minus plus or minus 1 M cha is measuring something else and she measures the length of that object the length of that object to be 100 M plus or minus 1 m who do you think has more uncertainty who do you think has more absolute error who do you think has more absolute error or CH uncertainty or absolute error right is this part after the plus hour minus this is the one over here who has more uncertainty or absolute error my name is Captain shers thank you for having crush on me I hope that Crush translates into marks that happens I will be more happy okay one and one both are same oh my God so definitely definitely both have the same same uncertainty or same absolute error both have the same absolute error agree with this no not pandu not Champa both of them have the same absolute error think about it I mean for pandu in 10 m the uncertainty is this much 1 M but for cha in 100 meters the uncertainty is still the same if you look at it relatively if you look at it relatively who has more error or who has less error think about it come on guys for pandu in 10 the uncertainty is only one for Champa in 100 the uncertainty is one so I think cha is more accurate as compared to pandu so in fact we have a term called as relative error yes so relative error for Champa relative error for Champa will be error is one in 100 100 whereas relative error for pandu is 1 in 10 which is slightly higher in fact you can also write something called as the percentage error where you take this number and multiply by 100 it becomes 10% in this case the percentage error will become 1 by 100 multiplied by 100 which is 1% kind of makes sense for Champa 1 is 1% of 100 yeah correct hardly any error for pandu for pandu one is 10% of 10 yeah so this is more error so pandu has relatively higher you know percentage error or relative error so which one is more important I feel it is the percentage or the relative error which becomes more important while you know analyzing who is more accurate or who is more precise yeah is that clear everyone awesome so let's define the terms let's define the terms if you have any measurement which is given by a plus or minus Delta a any measurement the absolute error the absolute error is just given by is just given by delt which is also the uncertainty in the measurement uncertainty in the measurement relative error relative error is how much is that uncertainty upon the original value it's always a fraction like over here 1110th 100.5 16 1,000 like that so it is a fraction whereas the percentage error is nothing but the relative error relative error multiplied by 100 so it is nothing but Delta a by a multiplied by 100 all that is called as your percentage error is this point clear is this point clear yes awesome so glad so glad say ASA you understanding everything perfect uh is NE students can also watch it but we have a neat English Channel with Anon English watch it over there I'll be starting the series very soon okay yeah can you crack J why not TT you can definitely crack J who said that you cannot crack J I mean why should that be even a question first of all I'm not able to understand okay now sometimes you do not know the uncertainty sometimes you do not know the uncertainty so easily in fact you to find that uncertainty and for that what happens is the student performs the experiments multiple times or multiple students perform the same experiment so when multiple readings when multiple readings are taken then how to find the relative error percentage error Etc the logic is as follows you take down the readings reading one reading two like that reading number n reading number n after that what you do is find the average value of the readings find the average or the mean value average or mean is one and the same thing so it is nothing but you know you take all these numbers R1 + R2 like that till RN till RN and just divide it by n the number of quantities n number of quantities keep this aside now what you do is at every single place at every single place what you do is for R1 find how different is R1 with r average and just take the modulus of it so do this R1 minus r average R2 minus r average or R mean do this for everything RN minus r average modulus that means you are not worrying who is more who is less just taking the posi difference this is called delt R1 this is called delt R2 like that last one will be called delt RN these are called as absolute absolute errors absolute errors how much is the deviation from the most probable value you have some numbers you find the average value from the average how much are you deviating so you taking the absolute deviations from the most probable value what you do now is basically find the mean absolute error mean absolute error when I say mean absolute error it is basically the average of these things so you take all these numbers and divided by n that's all basically it is delt R1 + Delta R2 like that delt RN so that will give you the mean absolute error hence our final answer our final answer will be something like this it will be this most probable value which is our average and then you will have plus or minus which is mean absolute error mean absolute error the this is how you will write down the final answer let's take an example and then let's understand it let's take an example to understand this okay when you have multiple readings here is the example what are our readings 12 10 9 7 readings 12 10 9 7 so let's write it down 12 is one number these are your readings these are your readings okay 12 10 9 and 7 what is the first step take the average value take the r average value or the mean value so the readings average value will be nothing but there are four readings so divide it by four what are the readings 12 + 10 + 9 + 7 how much is it coming out to be how much is the average value coming out to be put it up in the chat box right away right now my dear Warriors put it up right now my dear Warriors how much is it coming out to be come on yes 9 + 7 come on do it yes how much is it coming out to be everyone put it up in the chat box quickly yep very good very good some of you have got it yes very nice finally very good 9.5 very good perfect because the final sum will be how much it will be nothing but 3 uh 8 I believe yes so it will be 19 divided by 2 which is 9.5 perfect now comes the next step next step is what you have to find the the absolute errors so the absolute error means you subtract 12 with 9.5 12 with 9.5 then 10 with 9.5 then 9 with 9.5 then seven with 9.5 7 with 9.5 but take the modulus everywhere everywhere how much will this be this will be 2.5 correct this will be .5 this will be also .5 this will be nothing but 7 yeah correct this will be 2.5 perfect check this out everybody with me what is the next step going to be you are going to take the average of these so the mean absolute error the mean absolute error this whole thing divided by four this whole thing divided by four 2.5 +5 +5 + 2.5 come on my dear Warriors how much is it quickly yep yep yes 2.5 +5 is 3 3 + 3 is 6 6 divided 4 1.5 very good perfect so see if you got the answer as your 1.5 so my dear Warriors my dear Lions what will be our final answer going to be what is our final answer going to be it is going to be 9.5 9.5 plus or minus 1.5 plus or minus 1.5 got it that's the answer that's our final uh most likely answer it will be most likely 9.5 plus or minus chances are there somewhere between uh you know + 1.5 minus 1.5 from 9.5 if you talk about the percentage error if you talk about the percentage error it is the error which is there which is 1.5 upon the most probable value which is 9.5 the whole thing multiplied by 100 come on my dear Warriors my dear life what is the answer going to be 15 and 95 you can divide by five each so this will be three times this will be 19 times into 100 so approximately how much is that percentage error going to be come on 19 1 and 19 so you have 11 then 0o 5 so approximately 15 something just just check this out 15.7 or something 15.7% just check this out 15.7 yes perfect that would be the percentage error understood how to solve these problems how to find the absolute errors how to find the final answer and then finally calculating the relative and the percentage error very very simple right so we have learned what the basic errors are what the basic errors are how to do the calculation of it okay now do you know that basically you can also add and subtract you can also multiply and you know divide with errors you can play around with errors that is the last last subtopic of how to handle the combination of Errors what do I mean by this let's understand let's understand say for example I have the number let's say uh let's say you know 8 + minus 2 plus if I had to add you know 3 + minus 4 okay I want to add this second problem you know 7 + minus 5 2 + minus 2 but I have to subtract them basically I have two readings and I want to combine them together either by addition or by subtraction subtraction is also combination I'm combining seven and two together they both have some uncertainty so what is the final uncertainty in them interesting result whenever you have addition and subtraction always remember do the normal math for the main values main values these absolute errors which are there absolute errors are there you always add them always add absolute errors always add absolute errors the other thing just do the normal maths meaning for example over here 8 + 3 is basically 11 put plus or minus 7 - 2 is 5 put plus or minus only for this error part you just follow this rule always add 0. 2 and4 will make it 6 0.5 plus2 will make it 7 lot of students do this they subtract this also that is wrong 0.5 -2 is wrong 0.5 +2 is correct that is the catch yeah always always V that is a separate uh whole entity all together screw gauge and micrometer and all that experimental physics we'll do it sometime later as a special class in fact uh I have done a special class on it on the channel itself all the instruments together all the experiments together first time on YouTube okay is it done you can check that lecture out if you want to but that is not so important right now generally experimental physics is done towards the end of the syab okay don't worry about it now all right so if this is clear find the error in the following combinations let's see if you guys can figure this out 20.0 plusus 5 7 0 +us 0 0 1 sorry 0 1 what do you think the final answer should be what do you think the final answer should be come on do this okay do this then you have 6 0.0 + -.1 minus 2 0 + minus three you have to subtract this come on my dear Warriors my dear Lions what is the answer for this come on think about it yeah Tamil just a couple of more minutes and we are done just do the normal maths first 20 and 7 is 27 60 minus 20 normally is 40 now go step by step whenever the absolute errors are there what will you do you'll always add whether it is addtion or subtraction so. 5 + 01 is 51 here .1 +3 is basically 4 but there are some catches involved over here and I'll tell you what it is the decimals the decimals whenever you add and subtract what should you do you should be be very careful about the decimals The Final Answer should contain the least of the decimal places this has one this has two this has one this has two so what should the final answer contain one decimal place so hence the answer will be 0 answer will be 0 Z here also there is a problem this has two decimal places this has one decimal place I can't keep two I have to keep one decimal place so my dear Lions what are you going to do approximate it to one decimal place which is 0.5 single decimal place got it that is a catch and that's why our final answer to this question will be 27.0 plus minus5 no 51 if 51 is there in the answer you will cross it out you will eliminate it you will get Negative marks otherwise cool here I don't think we need to do much I mean it's pretty much obvious single decimal place so single decimal place single decimal single decimal so plus minus okay this answer is as it is 40.0 4 plus minus perfect nothing wrong here because both had one one decimal place each so that also matters yeah this is a common mistake this kind of questions have come in J so this is a proper level two question guys is a proper level two question moving on to the next one uh yeah this is beautiful question actually you will love this question this is level two properly I mean previous one I won't even categorize it as level two this is level one okay just small trick if percentage error in the measurement of the length of an object is 4% if it is broken into halves then the percentage error will be if you answer this I will be really proud of you so basically imagine there is a object there is an object okay and it has some uncertainty in it it has some you know uncertainty in it this has some uncertainty in it this is that uncertainty you break it into two equal halves you break it into two equal halves so what is that percentage error which will be there in each one of them what will be that percentage error in each one of them come on my dear Lance if you get this I will be really really proud for sure I should book a seat for all of you in the I Bombay Madras Delhi campus hello mati let's see if you can figure this out okay I'll tell you one simple thing just observe assume this is L1 plus minus Delta L1 this will be also L1 plusus Delta L1 after breaking it into two parts if I combine them together L1 + minus Delta L1 L1 +us Delta L1 if I add them if this is L +us Delta l I should get L plusus Delta L I should get back the original Rod the original object so if I use that logic over here think about it I do not know what is L1 I do not know what is L1 but I know the final answer assume it is 100 units error is 4% error is 4% so is it not like saying it is 100 + - 4 100 plus - 4 so think from this what think these both will add to give you four so Delta L1 is two correct so what is the percentage error what is the percentage error in each one of them the absolute error upon the most probable value into 100 what is this 0 0 cancels this goes with this this is still going to be 4% yes the answer is B it is still going to be 4% what a beautiful question and I proved it to you logically very good tarun Tes okay don't spam but yeah you got it I know you guys are very excited to Mark the answer as B isn't it fascinating generally what people think is you know the error will get divided it will become 22% actually what becomes half what becomes half absolute error did you see that absolute error became half yes when I divided it the absolute error got divided but even the length got divided so the ratio remained the same 50 by 2 100 by 4 is one and the same thing that's the reason cool let's move on that's why it's level two oan let's move on last part multiplication and division now I'll tell you what multiplication division and in general for any powers and basically Powers the rules for them is same the rules for them is same I'll tell you why example I write power is force into velocity or let's say velocity is displacement divided by time or let's say kinetic energy is half m v² or let's say you know uh time taken to fall time taken to fall is root of 2 H by G multiplication division in general any powers this works the rule is as follows the rule is as follows always to find out the error in the final quantity if each of them have some error mean mean Force has some uncertainty velocity also has some uncertainty power will also have some uncertainty same thing displacement time have error velocity will have error Mass velocity have error kinetic energy will have error H and G have some error T will also have some error so the question is how do you find that so the step is as follows always express it as Powers express it as Powers meaning for this case it is p is equal to F to 1 V to 1 in this case v is equal to S to 1 tus1 just like in Dimensions you bring it on the top here kinetic energy is half M to 1 V to 2 express it in Powers here < tk2 is outside it is H raed to half G to minus half G to minus half are you able to see that okay express it in Powers now what is the next step the next step is as follows the relative error in this physical quantity will be you write down the relative errors separately for each one of them Delta V by V Delta F by F same thing over here the relative error in the final quantity will be relative error in each quantity you put them separately over here same thing here also relative error in kinetic energy relative error in Mass relative error in velocity same thing over here relative error in time will be equal to relative error in h relative error in G now what do you do add subtract what do you just do over here the answer is as follows always add don't subtract but you multiply with the powers before adding so force is raised to one so 1 into this velocity is raised to one so one into this and just add them that's it as simple as that always take the modulus of the power displacement is raised to one time is raised to minus one don't take minus one take modulus only and then add here also mass is raised to 1 velocity is raised to two add them that's all here let's do it height is raised to half G is raised to half only always take the modulus positive value and just add that's all you need to do as simple as that as simple as that is it clear so whenever multiplication division powers are there what you do first express it in the power form just like you did it for d Dimensions everything on the top forget the constants forget the constants write down relative errors add them but before adding multiply it with the Positive values of the power modulous values of the power exactly so imagine if somebody tells you imagine if somebody tells you area of a circle has the formula p piun r squ and radius has has a percentage error of let's say 6% then then percentage error percentage error in area is how much very very simple question let's see how to do this area is p pi r squ just like over here it is expressed in power form forget the constant so the relative error in a will be only one term is there so delt R by R nothing to add or subtract the power of R is 2 so you multiply by two that's it best part I can also write it in terms of percentage because if I multiply by 100 it will become percent If I multiply by 100 both sides it will just become percentage now wait a minute the percentage error in the radius is 6 oh so 2 into 6 is 1.2% so that's it that's the percentage error in area percentage error in area is 1.2% that's how simple this is clear everyone okay let's see if you can solve the next level one question error in the measurement of the radius of the sphere is 2% what is the error in the measurement of the volume what is the error in the measurement of the volume yeah yep come on what is the formula for volume it is 4X 3 piun R Cub so Delta V by V this is a constant forget it is delt R by R but three times if this is percent this is also percent so 3 into percentage error in the radius is two so hence the answer is 6% hence the answer is 6% percentage error in volume now please bear this in mind whenever we use these formulas in general so if p is equal to some constant P1 ra to Alpha U into P2 ra to Beta P3 ra to gamma so on and so forth and then you write Delta P by P is equal to forget the constant Alpha Delta P1 by p1+ Beta Delta P2 by P2 plus gamma's modulus Delta P3 by P3 so on and so forth this is valid only if only if the percentage errors are small percentage errors are small like 5% 6% 2% 10 like 8 %. 5% 6% if it is small only then this formula is valid otherwise you have to go with derivatives otherwise you have to go with derivatives yes like for example you will learn this later on also like there was a question which was asked in J Advance this is like proper level three kind of question where when you learn mirror formula or lens formula which is 1 by V plus 1 by U equal to 1 by F object distance and image distance have an error what is the error in the focal length so over there you have to use proper derivatives like this V to minus1 + U to minus1 IS F to minus1 and now you differentiate this with respect to something you differentiate both sides with respect to something so V to minus one's derivative using chain rule will be -1 V -2 into DV by DX + -1 into U -2 into du by DX is equal to -1 into F -2 into DF by DX -1 -1 -1 cancels so DX DX DX also cancels so V to -2 DV + U -2d U is fus2 DF so from this you will get DV uh by v² + du by u² is equal to DF by f s so you know you can think as if this error this is some error focal length will have some error so if you substitute all the values you will get this so you might have to do some kind of a derivative approach or some different approach if you know the problem is not of some standard value or Beyond you know I have you might have to think literally out of the back box literally out of the box this is a proper level three question now let's look at one more question over here some quantity is raised to half 2 3 -4 a b c d their errors are also given this is level two question J meanss it was asked what is the final error in P what is the final error in P come on my dear Lions you can easily do it P is a to half B to 2 C to 3 D to minus 4 so think about it Delta P by P will be Delta a by a Delta B by B Delta C by C Delta d by D what are the powers half then two then three and then four and then just add them that's all you need to do that's it and everything is in percentage so half into Delta a by a a has an error of 2% plus 2 into Delta B by B it is having error of. 1% 3 into Delta C by C 3% four times Delta d by D which is point 5% come on do the math it is .1% plus 2% plus 3 3 is are 9 so 9% plus 2% see how much is it coming out to be my dear lines 0.9 + .1 is 1 1 + 2 is 3 3 +2 is 3.2 so it is 3.2% let's see yes option C C for Captain perfect it is matching it is matching everyone clear all right how about doing level three question I think this should be one of the last questions for today's class yeah this is the last question and level three question shall we do this shall we do this are you all excited because if you do this that's it this chapter is done dusted salted for all of you all because you you attended today's class in J Mains January attempt your four marks to eight marks are secure in your pocket nobody can take it from you in J Advance one question might come on this as a combination with other things who knows all right let's solve this side of a cube is this mass of the cube is this the density is how much well density is mass by volume volume is side length Cube oh so therefore density is mass ra to 1 a to minus 3 okay that means if I go error wise Delta row by row so if I go error wise I'll put it over here Delta row by row is Delta M by m Delta a by a A's power is three M's power is 1 so I just have to add them okay perfect so let's see what can we do over here Delta M by m Mass has some error how much Error 1 G out of how much 2,000 okay put it over here plus 3 into Delta a by a Delta a change in the length 02 upon how much 10 perfect then the density is how much okay the problem is how do I solve this because I don't don't know row this will just give me percentage error I think the question is not that okay fine you can also find percentage error that's a different story but I want to find Delta row also you know that is my aim so I have an idea come back over here from this density is most likely density is mass by side Cube Mass was 2,000 side length was 10 so 10 Cube 10 cube is th000 2,000 by 1000 2,000 by 1000 that's just going to be two 2 G per Cc or 2 G per CM Cube oh perfect I got row row is basically two row is basically two perfect I can just if you want multiply it and then find the value of delta row also over here so Delta row will be if you multiply by two this will be 1 by 1,000 plus 3 2 are 6 6 2 are 12 but shift two decimals so it will be .12 and one more decimal so it will be 012 012 or if you just don't like it no issues 3 into 2 into 2 into 10 ^ - 2 / 10 so this will be. 1 plus okay what we just do 3 2 are 6 6 2 are 12 and 12 into 10^ minus 3 so that will make it 0.012 so this will become correct I hope this is fine yep yep yep 0.013 that is gam per CM Cub that is gram per CM Cube so hence our final answer of density will be our final answer of density will be 2 +us 013 G per CM Cube that is our final answer this is how I'll write it so most likely the density will be two but there is an error margin which have kept uncertainty which have got it from here is that absolutely clear my dear Lions yep everyone okay perfect great great yeah this is how you solve the questions and uh yep 013 so one small thing request please like the session if you have not done it yet subscribe to the channel number two uh there is a link which is there in the description box let me just show that to you it's for your benefit only so going down going down do you see click here for Jungle Book what are you going to get animals out here maybe we'll find out so you go over here uh provide accurate details why am I getting this okay let's put something I'm from bangaluru let me see if I get bangaluru yes bangaluru continue and here I will get the Jungle Book link just click on this I have logged in before that's why if you don't log in you have to create your free account and here you will get the YouTube link the date on which it was conducted the PDF notes will be uploaded later on DPP as well okay so whatever I write on the screen will be available here so every time you don't have to search for the PDF notes dpps I took in that extra effort for all of you so that everything is at one place after sometime I will add more tabs when you know I get some time to consolidate all the different types of classes our old Advanced Class VI class SRM class bits class IAT class ugwe class so everything is at one place in this sheet this is why we call it as The Jungle Book literally all the kinds of animals insects birds everything are there over here got it that is what it is okay so I'll upload it Dakar very soon the DPP everything all right all right without blinking the eye wow very good awesome so this is how our lectures are going to be in fact if you have anything to say please let me know in the comments all right I'm going to start from the scratch do level one level two level three problems also with pyq also are there my own questions are also there concept is also taught and everything is in one shot marathon in detail without skipping anything that's the best part about the roar series if you are serious about J 2025 2026 this is the only YouTube series that you will need after this self study use your books coaching material if your coaching is not good watch it over here right that is the reason why I'm conducting the classes many YouTube channels are there in Hindi for English you have us and I will make sure that I give you quality content okay so stay tuned on the channel by subscribing liking and commenting I want your love and uh comments and likes obviously I want it I will be open about it and you have to give it as simple as that it's a very simple give and take okay thank you so much for all the quality content do not forget to subscribe do not forget to like and support the channel bye-bye Captain signing off asista

Channel: Vedantu JEE English

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Id: SZIeIjR7u-g

Length: 239min 37sec (14377 seconds)

Published: Wed Jun 05 2024