Mechanical Properties of Solid L1 | Elasticity Modulus & Stress Strain Curves | 11 Physics JEE 2023

we are going to talk about mechanical properties of matter and yes we are going to talk about elastic bodies so elasticity has a very very important role to play not just in our daily life but there are so many phenomena and so many applications of elastic properties of matter all of this with me sri as your physics master teacher going live hi sweet hello ramya and let me quickly brief you what we are going to do in today's you know nurture lecture one of mechanical properties of matter now we're going to start with what is deformation what is the different types of you know behavior of matter then we will also go to different types of stress and strain yep you take stress during the exam and there is stress in physics too you're going to talk what is stress what is strain what are the different formulas the most important law that is hooks principle the hooke's law for elastic bodies and yes then we're going to talk about the different types of modulus of elasticity for the three kinds of deformation and then we'll go to the energy store and finally we'll end the class with stress strain grafts and their applications so those of you do not know me i am stressed uh some of the students also call me capitol stress yep because probably i'm the captain for your journey towards success when you're going to crack g2023 so welcome aboard uh having thought almost like for more than 10 years i know what it takes to get into iit i know what kinds of struggles you need to do in this course of two years so stay with me in nurture series because this is a long term batch for all of you on youtube which is going to cover the entire 11th standard syllabus so it doesn't matter even if you're a 12th standard student or even if you're a 9 standard student who wants to study you know 11 standard portions you're all welcome aboard so for that you need to first of all hit the subscribe button in case you haven't done so even till now because then you will miss the classes if you have not yet subscribed and also a lot of lot of thanks for smashing that like button down there hello aishwarya hi ramya hello harita welcome aboard a warm welcome with all your lovely hearts nice to see all of you out here in the next session this is on demand class reason is just last week i conducted a poll on our youtube community what is the next class you want and all of you are like sir we want mechanical properties and then you want thermo and fluids and all of that so i have listened to you so we will do mechanical properties today it's a small sweet simple chapter and if you have studied this in school and if you still have doubts trust me this session right now which are going to attend will help you it will give you some more knowledge it will give you a lot of problems practice and if you have no idea still this will obviously help you because this is eventually going to come and we're going to have so many more sessions in the days to come so let's begin this class and uh yep let me also tell you all the pdfs will be uploaded very soon on our enthused telegram channel and the link is there in the description box below so what is elastic behavior okay you might have heard about rubber band showing elastic property yep thank you rahul krishna it means a lot very good i'm so glad that you are back to the next class too so elastic means it comes back to its original shape or size like look at this rubber band you stretch it leave it comes back right it does come back the tail of a dog have you heard about that thing the tail of a dog never straightens if it's curved no matter what you do you hit it you console it you advise it you iron it have you tried ironing the tail of a dog don't do that it's cruel okay so no matter what you do the tail of a dog even if you try to turn it if you twist it if you try to straighten it again comes back to its original shape that's how it is yep it is but plastic behavior is completely opposite like clay look at this beautiful example of clay you might have played with clay in your childhood or even maybe now or cheese on your pizza you bend it leave it it stays there chewing gum you bend it leave it it stays there it's not going to come back right so these are plastic bodies elastic is a property where the body regains its shape when deformed and plastic is the property where a body does not regain its shape when it is deformed it does not come back to its original shape and size that's what it is very good ramya hi chandra welcome aboard now there are different ways in which you can analyze why do bodies actually come back to its original shape or why do they not come back to its original shape and size if you think of any object beat this book beat this remote beat my hand beat this watch beat your table beat a steel ball beat a rubber ball it's all made of molecules and molecules are joined together with bonds so simple way to analyze it is imagine the molecules like these masses and the bonds like the spring if two bonds try to come close to each other it's like in a movie the hero tries to go very close to the heroine the heroine is like go away duryam is a rudy basically maintain distance social distance now if the hero goes really far away the heroine is like hey come back i'm missing you so that's what happens between any two masses if they go far away they are pulled back elastic forces the spring-like forces push them back if they come very close then they're again pushed back to their equilibrium position now every body behaves in this manner so when you apply any external force like let's say you hold an object or you push an object or you pull an object or you just you know press something then these bonds get compressed or elongated depending on how you're pulling or pushing it so exactly what happens is these molecules you know they come close or they go far away and these spring lug forces come into action so when you remove this force if you remove this force the spring like forces will push them back over here and into their original shape and size so this external force is your deforming force i will write it down over here this external force so this is basically your oops where did it go okay so this external force this external is basically your deforming force and your internal forces together will try to restore it so that's why it is called as restoring force when you remove the deforming force the restoring force pulls it back in elastic bodies is the restoring force present or not present put it up in the chat box hi rr sanjay hi santosh s yes great look i just conducted a video for strategy for the physics examination just watch it okay just connect it few minutes back so in an elastic body what do you suggest is there restoring force or is there no restoring force come on think about it obviously there is restoring force but in plastic bodies like clay cheese or anything which deforms and does not come back is there any restoring force present think about it it does not come back so there is no restoring force so in those kind of bonds if you compress a spring that's it it stays compressed that's it gone permanently deformed it's like okay give up so in plastic bodies there is no restoring force present the springs get broken or the springs are ineffective in pushing it back that's what happens hence i will classify the objects in the following categories based on the elastic properties first is elastic body the second one is plastic body a plastic body does not regain its shape and elastic body has two more categories perfectly elastic and partially elastic perfectly elastic means you pull it it comes back to the exact same shape and size there is no minute difference also even at nanometer level you pull it stretch it or compress it it comes back exactly the same way it was but actually speaking there is no such body most of the bodies show that kind of behavior okay you cannot distinguish so we call it perfectly elastic but many objects okay show partially elastic behavior as in when you bend it stretch it or deform it it comes back but not so much so it is not perfectly plastic it's not perfectly elastic so somewhere in between is that understood by warriors yep yep i hope this is clear okay so ramya slam slide i used yesterday in mechanical properties lecture four uh i'm not sure uh okay so yesterday i did not conduct any class on mechanical properties this is the first class okay cool now here is your first question which of the following substance has highest elasticity is it rubber is it steel is it clay or is it wood come on very good chandra very good alien mishra very good ulna what what do you think which of the following substance has the highest elastic property is it rubber is it steel is it clay or is it wood very interesting question some of you saying steel some of you saying rubber some of you saying again steel okay students are confused between steel and some of you are confused between rubber yep so taiyo it's all uploaded in the telegram channel yep if you join well the correct answer is actually steel it's not rubber obviously clay is not even elastic wood no it breaks off i mean like if you bend it it breaks that's it gone okay it's brittle rubber and steel you are confused see rubber is elastic but not as elastic as steel if you bend steel like the one i can show you probably over here then you know it tries to regain its shape and size see look at this steel scale i bend it see so much of bending it comes back you can see it came back to its original shape and size but rubber when you bend it it comes back but it might show some plastic behavior it might bend permanently as well so rubber is not as elastic as you know steel that's what the problem is with the rubber it can show if you stretch your rubber band too much you have to have seen that the rubber band becomes elongated yep or your pants if you if you have an elastic band you stretch it too much or you become too fat you would have noticed you become too fat for example or some friend of yours would have become too fat suddenly after one month you will realize if you become thin then the pan no longer fits you because the rubber has already stretched have you noticed this have you noticed this if you become fat and suddenly become thin you would have noticed your pants no longer fit you it becomes really big okay anyways now let's talk about stresses what is stress stress is essentially intensity of the force let me tell you what stress is stress is the intensity intensity of the force i'll give you a very simple example and you will understand it arun says yes looks like arun was really fat some days back and then he has seen that his pants no longer fit him very good so here we have a cross section imagine these arrow marks together show you the forces direction together this is 10 newton force okay together this is 10 newton force now i take a small cross section and there are you know it's not as big as this smaller and there are same arrow marks but more in number but in spite of that they together add up to 10 newton they add up to 10 newton because now they're on the smaller area so they have to be closely packed so that's why more number of arrow marks but you know close to each other still the total force is 10 newton you will see that here the force is distributed on a large area here the force is distributed on a small area so when the force is distributed on a small area it is more intense it is intense the density is more okay the intensity is more here the intensity the intensity is less so here i would say the stress the stress is going to be less here the stress is going to be more so the compactness of the force if the force is on a big area less stress the force is on a very teeny mini area more stress i'll give a simple example okay let's try this if you have a pen if you have a pen everybody come on let's do this i have a pen and this is a hand and i'm just going to apply some force from the top see this hand from the top it's going to apply the force just do this on your palm are you feeling the pain if you're feeling a vein raise your hands up okay hello i know i am aware of that problem there are some uh issues like i said it needs to get uploaded it's going to take some time maybe some of the sessions would not have been uploaded it will take some time give give me a week by this week i'll make sure it is sorted okay yeah so okay okay ramya no problem so do you feel that pain yes now reverse that pen and hold it like this now apply the same force now you don't feel the pain you reverse the pen yeah why is that same force but the area on which the force is applied is different when you do this the pointed point is touching your hand or your palm then you feel the pain because the stress is more so that's what stresses did you now feel stress how many of you felt the stress yeah so that is what stress is stress is the force acting per unit area applied force by the area area is less stress is more force is more stress is more that's what it is perfecto and yes you realize the moment you reverse the pen there is no stress there is very less stress you don't feel that pain perfect or excellent now there are three kinds of stresses yep because there are three kinds of deformation that happens every day around us any kind of deformation can be classified into one of these three categories at a minute level anything any deformation you hit somebody his face gets deformed okay or basically you press somebody his body gets deformed all these deformations come under one of these three categories the first category of deformation is called longitudinal longitudinal means you stretch or pull along the length or push it along the length like for example the column in your house it gets pushed it gets compressed because of the weight of the building or if something is hanging let's say you hang your hands are under that stress along that length that is called as long longitudinal stress longitudinal stress look at this are these two diagrams making it clear what is longitudinal stress but there is a small difference between the two the top one is tension the bottom one is compression ragam i'll definitely let you know about your state in the end i'll show you how to enter into 2023 vip subscription okay don't worry all right so this is tensile stress this is compressive stress i hope it gives you an idea what stress is now the uh yes now rahul very valid point isn't stress and pressure the same thing no it feels the same but it is not technically the same thing i'll tell you i'll give an example imagine this is a pandu okay let's draw pandu's hands this is pandu's hands like this very thick pandu this is a very thick pando okay this is his hands his biceps are very large he just does hand exercises he does a lot of pull-ups push-ups and all of that very hard working punch now don't you think his hands are under longitudinal stress his hands will have some cross-section so this is the cross section of pandu's hand this is the cross section of pandu's hand so obviously there will be forces which are acting along that cross section so that force which is perpendicular to that area upon the area of cross section is basically called as the longitudinal stress in general the symbol for stress is the sigma usually you will use the symbol sigma but since this is longitudinal i will put a subscript l o ng that signifies it is longitudinal stress that's it this is the formula for the stress developed in a rod which is pulled or which is compressed and what would be the unit of this the unit will be newton per meter square as simple as that or you can also use pascal both units work newton per meter square or pascal production because this is a long class that's why it's seven o'clock yeah this is a little bit long class because i want to complete this chapter and this chapter is simple sweet and short so we can finish this within two hours is that clear so that is longitudinal stress the second kind of stress is bulk stress or pressure many students answer what is the difference between pressure and your stress here is what it is see imagine i give you like a cube okay imagine i give you like a cube i [Music] okay i apply force on this face this way on that face this way will there be stress in the cube obviously yes what kind of stress longitudinal stress should i call it as pressure no usually longitudinal stresses are associated with solids because you can see the forces act in a particular direction okay like when you pull a rod or you compress a column you can see the forces are in one particular direction then for solids you define something called as the longitudinal stress but for liquids there is no shape and size if you take a blob of water the blob of water the forces are there everywhere here here here here there is pressure everywhere if you take a chunk of air chunk of liquid chunk of any fluid there is forces on every side no matter where you go so the force which is acting per unit area is then called as pressure is that understood so pressure is used for fluids okay it's associated with fluids and it acts in all the directions but for solids generally the forces are in certain directions only that's why you use the word stress is that understood my warriors is that clear so for fluids you define something called as the bulk stress or normal stress and this is nothing but change in pressure change in pressure on a fluid that is called as bulk stress so sigma bulk again the unit is just pascal or newton per meter square as simple as that change in pressure you change the pressure it deforms you relieve the pressure basically changing the pressure it deforms so that's what it is look at this solid okay or look at this fluid you apply pressure from all the sides the volume changes you relieve the pressure again the volume changes so any changes of pressure changes the volume that's what bulk or normal stress does i hope this is clear now very good very good isaac the last type of stress because i told you there are only three kinds of deformation that is shear stress i'll give an example okay so here i have h c verma book okay this is my h c verma book and what i do you can see a lot of pages arranged over here yeah a lot of pages i hold it below and i hold it on the top i don't press it like this but in fact i do this i slide my fingers i slide my hand do you see that the pages of the book slide over each other do you see the pages of the book slide over each other you push it like that the pages of the book will slide over each other like this i hope you can see that that way or this way you can see that left side or right side so basically what has happened it has skid over each other there is sliding of layers whenever layers are sliding over each other that is called as shear that is called as shear example another example you take a knife okay you take a knife and you are cutting your birthday cake okay let me just show you another example okay you take a knife and you're cutting your birthday cake it's your happy birthday everybody's singing happy birthday song for you and you have no clue what to do that's what happens so you take this knife and you cut it through so when you cut it like this imagine what is happening the layers are going to slide so this layer which is there this is going to slide down with the adjacent layer so that is again shear yes so sliding stress correct him and freaky so when you cut it the layer starts sliding so that's the reason why it is called as sure perfect hello strategy join in bachelor welcome so how do i define this kind of stress it's simple so it is nothing but the force per unit area look at this beautiful example animation of what sliding stress or what shear stress is so again the shear stress i will put it sigma shear is the force which is parallel to the area notice this this is parallel to the area upon the area or which is sliding that's all so force which is parallel to the area upon the area which is sliding as simple as that three definitions done done adam let's move to the next thing which is strain stress is done stress is done let's talk about strain and then we'll quickly go to problems get ready strain strain is basically a dimensionless quantity which tells you how much fraction did the solid or liquid deform it's a fraction which tells you how much deformation occurred strain can be both it can be positive or negative strain can be positive it can be negative if it is positive it has basically expanded if it is negative it has contracted that is one thing and understand it is dimensionless so no dimensions very very important there are no dimensions strain symbol is epsilon or not it is nothing but a fraction it can also be expressed in percentage percentage as well okay now when i say a solid expanded by one percent it means maybe the volume was 100 now the volume became 101 so the strain will be one percent if the volume contracted from 100 it became 99 i would say the strain is minus one percent so minus means it contracted and one percent means if it was 100 it has now become 99 as simple as that so that is what strain is epsilon naught is the epsilon is the symbol so obviously if there are three kinds of deformation there will be three kinds of strain let's talk about it longitudinal strain so you take a column rod compress elongate it so the length will change so the longitudinal strain okay epsilon longitudinal will be change in length here i will put x divided by original length so what is x you can see that x over here this is basically x and this is basically l so it is l it is original is the original length and x is basically your change since this is meter this is meter if you divide it dimension wise there is no dimension as simple as that okay perfect so longitudinal strain is the change in length upon the original length that's what i have put it right over here hello karu prem kumar welcome aboard join in and thank you for liking the video it means a lot okay next deformation bulk deformation so we have bulk strain also what is bulk strain okay very easy if you have a volume of fluid solid whatever liquid you change the pressure the volume changes so bulk strain so epsilon bulk is delta v by v what is delta v it is change in the volume because it is associated with bulk bulk means in general collective property collective as a whole so the liquid as a whole so liquid as a whole what's its volume and how much did the volume change my that's all so change in volume upon initial or original volume that's what bulk strain is all about so original volume was v naught so you can see some gap that is the change in volume is that clear my warriors so ajay the class 12th revision timing will be 11 o'clock tomorrow for the marathon sessions for cbse term one okay very good morning third type what is the third texture remember i told you about shear sliding i showed you hc verma book sliding the layer sliding so if one layer slides with respect to the other layer and it displaces by x the area slides by x because of this force there is an angle which is created the distance between the layers is l so let me mark this so this is basically your sliding layer this is your sliding layer okay this is your sliding layer what is this l this is basically distance between the layers this x what is this x it's the amount of sliding is the amount of sliding okay or basically shear you can see this phi theta whatever you want to call you can call it as the angle of shear and then you define the dimensionless quantity as x by l how much did it move for whatever distance between the layers so the shear strain remember epsilon is strain this is shear stream is x by l which is also tan theta by geometry or tan phi whatever you want to call it tan phi you can see that and if theta is or phi is small then it is approximately five in general okay because this is very very small angle in general when you know phi is very small that's what you should remember is that clear yeah no problem no problem roshini i know usually my classes are at 7 30 but today i conducted at seven o'clock reason being i wanted to finish this chapter yep okay gaurav uh today i will come complete the theory part and the basic problems part but we will have one more class on this for just problem solving is that okay gaurav yep yes remove this is the new chapter yes okay shm also theory and basic problems and we'll have problem solving sessions on shm my aim is to make sure that we cover all the basics and simultaneously as revision will conduct problem solving classes all right cool thank you for all the love moving on so that was x by l which is fine let's start solving some questions coming up on your screen there is a spring which is stretched by a force the resultant strain produced in the spring is volume shear tensile none of the above no problem no problem children you can start from beginning even in a live class all those of you are joining in right now at 7 30 please rewind the session catch up to the current topic even at 2x speed or even if you continue live you can still watch it no problem okay great so what kind of stress sorry strain is produced in a spring which is stretched some of you are saying shearing okay thank you ignace i'm so happy that you are happy about me and so it means a lot all right trusty come on i hope you have coped up all right come on come on come on my warriors what do you guys say is it volume yep is it c well the correct answer is actually b i'll tell you why no it is not c it is not tension lot of students make this mistake that's why i deliberately put this question students think sir spring sir obviously it is stretching longitudinal tension tension is there sir correct but the tension is not there in the spring as such the way you are thinking it's actually the tension in the string which is connected ahead actually what happens the spring which is coiled the layers twist with respect to each other think of a spring as multiple disks one over the other this is a disk okay like this then let's say another disc over it okay then another disc over it like this so there are multiple discs you know over it okay now when you expand the spring what happens is each layer with respect to the lower layer turns relative to it so when you expand it basically twists that layer twists and that's why the spring appears to increase the distance between the two adjacent coils this distance increases so when it twists okay it turns the distance it moves away the spring coils away from each other that's what happens observe the animation you will make a sense out of it look at this these are turns these are sections think of like small small slices each turn will you know slide with respect to each other that next return will slide with respect to each other the sections of that coil twist with respect to each other so there is sliding action the slices twist so that's why it is sure a lot of students make that mistake but i hope now it makes sense look at the coils cross section there is a thick coil that coils cross section is turning that is turning so that is turning so that's why the distance increases that's what happens is that clear okay moving on to the next one one end of a uniform wire of certain length and weight w is attached to a point on the roof and another weight is suspended from it on the lower end if s is the cross sectional area of the wire the stress in the wire at a height of 3 l by 4 from its lower end is going to be okay i know that's a beautiful question let's try and solve this so let's see this is the rigid end let's say this is your wire okay maybe this is your wire okay and you have some weight which is attached down over here which is um in the roof and the weight w and is suspended from the lower end okay so weight wn is suspended from here this is weight w the question is at a distance of 3 l by 4 from its lower end so 3 l by 4 means here so at a distance of 3 l by 4 question is what is the stress over there let's figure this out now if you look at this cross section this cross section will have some tension force correct there will be some tension force what will be the value of the tension force j go in no bachelor wave starter will come in the end not now we'll first do fluids after this then we'll do thermo and then we'll do waves is that okay so this tension is balancing something what is it balancing think about the mass which is hanging below it this is the mass being supported correct this is the mass being supported by it okay so what is the total mass of this system which i have enclosed over here it's not just wn but also this much part how much is the strings mass over here what is the mass of this much part of the string for this much part what's the mass or what's the weight if this much is weighing w how much will this much weight remember the total length is l total length l i'll write write it over here for total length l it is w so for 3 l by 4 what is the weight going to be think about it obviously it's proportional for length l it is w for half length it will be w by 2 for 3l by 4 length what will this question mark be it will be 3 w by 4 so hence this weight is just going to be 3 w by 4 isn't that right so what is tension supporting tension is supporting 3w by 4 plus the w1 this is the weight which it is supporting perfecto now the question is not that the question is stress so the stress value okay so the stress value for longitudinal part is nothing but going to be the tension divided by the area so what is the tension it is 3 w by 4 plus w 1 upon what is the cross sectional area s so that's it divided by s so 3 w by 4 plus w 1 divided by s which is option c is that understood very good very good khan money very good excellent day proud of you by chalupa yeah that's the answer so you will see at different different points the tension will be different the stress will be different there will be a beautiful question coming up towards the end of the class so wait for it this has laid your foundation for the next question which will come towards the end okay so wait for that end question all right so moving on to the next concept hooke's law you should be regular or else you will start developing backlogs and you will start losing influence so make sure you are regular see we just spoke about stress and we spoke about strain now here is what i want you to understand stress which is sigma and strain which is epsilon this is stream they are very much related to each other if there is more stress more force per unit area it will deform more more the deforming forces more the strain more the changes in the dimension so hook observed that for most of the bodies okay within elastic limits the sigma is proportional to epsilon is that understood and that also means sigma by epsilon this was what was observed experimentally this is my experiments by hook and that ratio is a constant that constant is called as the modulus the modulus of elasticity now why do i use the word modulus does anybody know about this why should i use the word modulus zaya try to manage it but try to finish your homework in the night or during other days make sure your focus is on jay or need whatever competitive exam you're giving homework will come other students also have homework but you need to manage time now why is it modulus modulus means positive the reason why i've said modulus is because this guy over here can be positive or negative remember stress sorry strain when if it is positive it expands strain is negative it contracts so irrespective of that this constant is positive that means actually speaking we should put a modulus symbol over here yeah that's what it is okay so remember modulus of elasticity means it's a positive number doesn't matter whether it is expanding or contracting the ratio remains the same for both expansion as well as contraction that's what it means that's all it means the ratio remains constant irrespective of whether you expanded or contracted hi abbas welcome join in let's look at three different moduli why three different modular because i just told you there are three different kinds of deformation so obviously three stresses three strains three moduli so what do we have let's talk about it modulus of young or young's modulus why this is associated with longitudinal deformation longitudinal if you ever get confused think of a young guy who is very long what will you think think of a young guy who is a young guy or bachata this is bacha bachcha means okay young guy and he's very long this is young's modulus that's how you can remember young's modulus yes longitudinal that's how we can remember it very good so this young's modulus will be longitudinal stress upon longitudinal strain so strictly speaking this is that force which is perpendicular to that area remember stress was forced by area i just told you force which is perpendicular to that area upon strain strain is this change in length upon the original length that's what you will get this sense okay beautiful formula now you don't have to remember this one but any modulus is stress by strain you know stress is forced by area you know strain is changing length upon original length that's all you should remember very good oh my god that was quick use of symbols now bhagwan uh i think uh i have seen it and i have also informed the team just hold on uh i'll just make sure that it gets resolved within this week okay yes bhagwan sir all right so fair enough now here is the next thing that i want you to realize this force which you apply believe me is basically going to be related in a very special way to this delta l observe this let me rearrange let me rearrange and i will show you one very interesting thing okay let's move this uh you know let's move this over here so it will become y into delta l by l is equal to f perpendicular by area so take that area there so it will become y a by uh l into delta l is equal to that f perpendicular flip it here so i'll make this as force which is y a by l delta l is extension now tell me y is a constant a is a constant l is a constant force is some constant into extension is there a deja vu movement is there a deja woman do you remember something think shannon don't worry just leave a comment or just ping me on instagram and help you okay i'll help you find the micro course don't worry about it look at this this is a deja vu spring force is some constant into extension this term over here is like like spring constant this is like spring constant very very important so you should remember this value equivalent spring constant is y a by l remember this okay apart from remembering young's modulus is stress by string remember equivalent spring constant is y a by l very good like spring forces perfect y a by l y a by l keep saying this couple of times 10 15 times y a by l okay remember why bile just keep on saying it okay now one last thing what is this young's modulus young's modulus depends on whether it is aluminium whether it is steel whether it is stone whether it is brick so it depends on that material okay so it completely depends on the material just to give an example the young's modulus for steel is around 2 into 10 to the power 11 newton per meter square just an example 2 into 10 to the power 11 that's a huge value of young's modulus so if the young's modulus is more if the young's modulus is more you need more stress to produce that deformation that's what it means if i is more you need more stress to produce that deformation it's very difficult to deform it if it is less it's very easily deformed perfect young's modulus stress by strain but everything longitude pranish how about this leave a comment after the session is i'll definitely help you or contact me on my instagram handle stress underscore vedanta okay fair enough next bulk modulus come on everybody knows the formula for bulk modulus because all the formula are similar so bulk modulus let me just put it up over here bulk modulus will be what bulk modulus will be nothing but okay here we have it uh bulk stress okay bulk stress divided by the bulk stream and we all know the bulk stress is nothing but change in pressure correct it is change in pressure the bulk stream is change in volume by original volume that's what it is but there is one small catch when you write oops when you write this formula just imagine this i'll give an example if you compress if you compress something is delta p positive or negative you help me out with this if you compress something the change in the pressure have you increased the pressure or you have decreased the pressure so is the delta p positive or negative no cg a cj vowel breaking has got nothing to do with young's modulus you will see it in a bit you will see it in a bit okay that's completely different lot of people associate young's modulus with breaking that's wrong okay so if you compress something delta p is positive but delta v is negative correct change in the volume is negative because it has compressed volume has decreased but we know b is a positive number how do you make b positive just put a minus sign so always in this formula you will see a minus sign that's how you are going to remember it i'll give another example imagine another example where it expands if it expands then delta p will be negative because pressure will become less change in the pressure is negative but change in the volume will be positive negative by positive negative to make it positive put a negative sign so both cases if you put a negative sign you will be safe understood my warriors is that clear why we have put that negative sign a lot of you might have been wondering so that's the answer normal stress by volumetric stream bulk stress by bulk stream as simple as that let's start solving some questions but before that the last modulus which is also called as the shear modulus or rigidity modulus sure rigidity mean the same thing okay so shear modulus okay shear modulus or rigidity modulus one and the same thing eta okay some books also use the symbol g okay some books also use the symbol g so up to you whatever symbol you want to use you look at the question they won't confuse you with symbols they will give you the sure modulus of aluminium is this much so they will express it in words so you don't have to break your head so the shear modulus g or basically eta whatever you want to call it is shear stress upon sure strain shear stream and shear stress is that force which is parallel divided by area and shear strain i just told you it is just 5 or basically x by l whatever you want to call it so that's the formula for rigidity modulus very interesting force upon the area which is parallel to the surface upon the angle of deformation or you can also call it x by l that's the same ratio opposite by adjacent side okay perfect ready for solving some questions my warriors geared up okay because unless you solve some questions you are not going to get some idea very good very good attitude very good everyone what is gg eco rigidity modulus or shear modulus okay dinesh cool let's solve some questions the young's modulus of a wire of certain length l and radius r is y newton per meter square that should be meter square guys okay okay if the length and the radius are reduced to length by 2 and radius by 2 then the young's modulus of that particular wire will be how much y by 2 y 2 y 4 y let's see how many if we can do this within maybe 30 seconds not more than that let me put a 30 second timer come on my warriors i want all of you to answer this question the timer has started somebody's saying see i don't know jerob also saying see um aslam no the crash course which is starting today does not have recorded classes it will be live classes but if you miss a class from today then the recording will be available for you later on okay so it's a fresh batch starting today and if you missed any of the class even today's class you will get the recording even today or tomorrow okay till the end [Music] ah well the correct answer is actually b very good lot of you made that mistake very good harita very good company see young's modulus is only dependent on the material many of you thought sir young's modulus is forced by area divided by length by change in length change in length by original length osr area change length change here if these two change now the force will change young's modulus will not change it only depends on the material material is still the same only length has changed understand that many people make that mistake diva i just conducted a strategy session just one hour back watch it number one number two i've already mentioned my 12 standard classes will be tomorrow onwards before the marathon i've already conducted so many cbs sessions just for you so make sure you watch that strategy session okay and be there tomorrow at 11 o'clock all right hello nitin here is the next question if stress is numerically equal to twice of young's modulus the elongation will be how much very good diva don't worry i will be there okay just study for now till the night in the morning just be there in the session i'll take care of everything okay and just follow whatever i'm saying we are with you all right don't worry diva okay what do you think is the correct answer let's put up 30 seconds oops wait a minute 30 second timer just for all of you let's see how many if you can get this within 30 seconds again this has gone to 59 minutes my goodness okay there we go 30 seconds what do you think if stress is equal to two times of the young's modulus what do you think the elongation will be uh yes yes yes silva kamantan ncrt i have given you what and all you should solve just watch my strategy sessions definitely and if you still have some doubts please let me know uh diva i'm not sure if school will be so beneficial if you think it is worth then please go but if you think it's again going to be time pass and if you want some other input then i would suggest watch my session but if you think no i want to attend school plus my session then you can watch my recording that's the only other option left well the correct answer is twice the original length okay how many of you got that very few of you got it some of you said b some of you said c also i'll tell you why stress is given to me twice of young's modulus that's what is given now we all know young's modulus is stress by string now here according to the question stress is twice of young's modulus so yy goes so therefore 1 is equal to 2 by e so therefore epsilon is equal to 2 when this is 2 what does it mean it means the change upon initial so essentially what it means the change is 2 times of initial so it is twice the original length compressibility balaji is one upon bulk modulus so if you have seen the word compressibility okay if you have seen the word compressibility it is won by the bulk of modulus that's it so that's all so if it is more compressible okay so it is more compressible it has less bulk modulus it has very large bulk modulus very difficult to compress that's what it means islam the crash course will be in english okay okay next question coming up on your screen and here it is great okay two parallel and opposite forces each of 5000 newton are applied tangent to the upper and the lower faces of a cubical metal block of side 25 centimeter the angle of shear is how much the shear modulus i just told you right they always give you the shear modulus in words and this is what it is 80 giga pascal so the question is what do you think is the angle of deformation let's see how many of you can get this really quick so let me just draw the diagram just for you so here is our you know deformed body and i think this is the angle which i want to calculate here is where i have applied the force on that particular area a over here we all know g is sigma by epsilon sigma is force by area epsilon is nothing but tan theta or just theta so the question is what is theta so theta will be f by a g theta goes up g comes down so f by h so let's start substituting what's the force the force is 5 000 newton so five into ten to the power three what is the area actually the side is 25 centimeters so what will be the area of cross section 25 centimeter into 25 centimeter which is 25 square into this is centimeter square so 10 to the power minus 4 meter square so i'll just put 25 into 25 into 10 to the power minus 4 this g is 80 giga pascal so 80 so 8 0 giga kilo mega giga so 10 to the power 3 10 to the power 6 10 to the power 9 so into 10 to the power 9 fair enough now let's see what an all gets cancelled this 5 and 25 so this will become 5 so 5 into 25 okay let's get rid of it later on this 0 and 10 to the power 9 will become 10 to the power 10 this 10 to the power minus 4 and 10 to the power 10 will become 10 to the power 6 this 10 to the power 6 and test 10 to the power 3 will become finally 10 to the power 3 over here now 5 into 25 125 125 into 8 what is 125 into 8 that's 1000 right so this will become 1000 into 10 to the power 3 which is 10 to the power minus 6 what is this theta radians that's all so i think 10 to the power minus 6 here we have it option c perfect very good umadevi very good khan money okay definitely shanu i'll check it out definitely uh so salva manikantan i'll do one thing bacha because i'm conducting 11 standard class can you do anything just post your comment after the video ends i'll definitely respond to you just leave it over there i'll definitely help you out okay cool all right yeah right great so that's the answer now here is the next thing very good a massive rod hangs from a ceiling as shown find the elongation in the rod when it is in equilibrium condition here is it very interesting question the thing is many students fail to realize that the rod itself has mass so its own weight is causing the expansion it's not like the rod has a mass attached below and you have to just do weight by area that will give you stress and that will give you the change in the length no the problem is the own weight is causing some deformation now there is another problem do you think there will be equal stress throughout the road yes or no yes or no what do you think the same stress will be here here here here everywhere or do you think it will be different let's talk about that first because it's not so easy it will be same well then if it is same then most of you are wrong because i just told you that i am going to do a very interesting question after some time and here is where that concept comes into play think about it over here and over here and over here the tensions will be different i'll give you the best way to visualize this there is a pandu he's holding like this and another pandu is holding his legs okay and then another pandu is holding this guy's legs okay and then another pandu is holding this guy's legs something like this okay beautiful that's how it is if i keep these numbers one two three four do you think all the pandus will have the same tension in their arms well they have same tensions i can't comment on other coaching but you know from what my experience is it's not that great okay so one two three four what do you think it will not be same obviously one will be highest then 2 will be next 3 will be less 4 will be even less same thing is happening here the uppermost mass is holding the entire mass below so highest retention so t1 is very large t2 is normal t3 is even less so the tension changes within the road if tension changes will stress be constant or not constant will stress the constant or not constant obviously it will not be constant if stress is not constant strain won't be constant if strain is not constant deformation will not be same if deformation is not the same everywhere how can you just say it is mass by area and whatever nonsense no right you cannot so i think we need to first of all break the rod into small small parts think about it each element so basically what i am going to do i am going to consider each element okay i am going to consider each element of the rod i am going to see how much elongation is there in each element each elements elongation can be added dx dx dx and i will get the total elongation of that orbit did you guys get it my overheads why i am going to make use of calculus now yep this is a question on calculus it's not so straightforward okay everywhere the deformation is going to be different so let's just forget about the options and focus on solving the question this is a beautiful question so elongation of a rod due to its own weight so that's what the question is okay so it's basically elongation elongation due to its own weight and the reason i am dividing it into elements is because you know the stress is not constant so i am just going to take some element right over here okay this element let's say is at a distance of x from the bottom and let's say the width of this particular element is dx what's the width of the element dx so this is basically your original it's your original length of the element at a distance x obviously there will be some tension right at a distance of x there will be some tension in that particular element so if i ask you okay if i ask you what is that tension okay over here what is that tension which is over here why do i need the tension because i need to calculate stress then think this way the tension supports the tension supports the weight which is there below supports the weight below just like the problem which we saw some time back and how much weight is there below think like this think like this for length l the weight was capital m into g the for length l the total weight okay the total weight was m into g for length x how much is that weight for length x how much is that weight think think think carefully think think think um who said only 30 days back here somebody has fooled you only 30 days are remaining there are more than 30 days remaining chill okay we're going to complete all the syllabus number two i'm going to come up with one shots very soon just give me two weeks maximum yeah two weeks of time don't worry okay aspirant yep so by the way if mg is for lentil what do you think is the weight for x length obviously it's mg divided by l into x force or weight per unit length into the length mg into x divided by everybody agrees with this fact yep very good very good so once you understand this you know what is the tension tension is the weight which is supported below and the weight which is supported below is basically mg by l into x this is what the tension is if you know the tension you also know the stress because stress is tension by area that means it is m g x by l a so that's what the stress is perfect once i get to know the stress i think i can find out everything else use the definition of young's modulus young's modulus is stress by strain oh i don't know the strain let me think about it carefully for some time what do you think is the strain in this element many students write sir i know what is the strain it is dx my x guys you are wrong if you are thinking it is dx by x i'll tell you once again what is strain change in length upon original length what is the original length is it x obviously not in fact the original length is dx observe carefully for that element it has a length dx so actually speaking denominator is dx then what is there in the numerator in the numerator is the change in length of dx in the numerator you have the change in length of dx so let me assume that to be dl so what it means is that that element which had a length of dx it has changed its length by dl so every element changes length by dl dl dld if i add all those changes i get the total change in the length of the entire rod is that now clear my warriors think about it is that perfectly understood cool let's go ahead so let me substitute everything over here sigma is m g x by l a epsilon is dl by dx okay i don't need this anymore rearrange i think dx will go on the top i'll just rewrite it so m g by uh okay so we have l a into dl dx goes on the top x and dx are right over here i think i can shift dl there y below so it will become dl is equal to m g by l a y and here we have x and d x i think i know what to do next you can see it is in the integrable form if i put integral symbol here and here i can remove this outside the integral because all of them are constant values that's it so integral symbol on both sides integrating both sides i just have to substitute the limits so value of x will start right from the bottom most element till the topmost element so all the elements from 0 to capital l this radial is 0 to small l what is this this is your total extension small l is your total extension this l is the length of the rod is the length of the rod understand so here adding the small small extensions these are extensions of each element i will get the total extension so let's see what do i get okay everybody find till this point let's see what do we get i'll just erase this i no longer need it dl's integration from 0 to l will be l and then i'll put 0 so l minus 0 mg by l a y integration of x dx x dx integration is x square by 2 correct x raised to 1 plus 1 by 1 plus 1 so x square by 2 so it will be nothing but capital l square by 2 minus 0 square by 2 perfect this is 0 l and l cancels so i will get m g 1 of the l goes uh here and 2 a y and this is l so this is our final answer hi salvan good evening bacha is that clear so what a beautiful question on integration and its application and it's very important to understand the flow of thought we started by saying stress is not same because tension is different the first thing was to identify tension is different by feeling if you felt wrong that's it you go wrong then we understood okay every element will have different strains and then i use the definition of young's modulus and i substituted everything and this rest is math by rearrangement i integrate it with proper limits that's it you get the answer perfect that's the answer mgl by 2a y perfect very good at your vermont moving on to the next part we all know that a stretched bow has some energy stored with it right any deformed body tends to regain its original shape so it has some energy stored with it potential energy but do you think plastic bodies have energy stored with it let me know in the chat box plastic like clay cheese anything which you deform leave it it stays there do you think plastic bodies have energy stored with it no right elastic bodies have stored energy in it so that's why i call this energy as elastic potential energy like in the spring so a spring which is deformed has elastic potential energy plastic bodies do not have any energy stored in them so we can find that out it's not that difficult and i'll tell you how to find it out i think i just told you that a rod a body which is elastic is very much similar it's very much similar to nothing but a spring which has been stretched by x i just told you the spring of natural length l and constant key it has been stretched by x and i just told you the equivalent the spring constant is nothing but y a by l so what is the energy stored in a spring what is the energy stored in the spring u it was nothing but half k whatever is the spring constant into extension square correct so how about using that same formula and finding how much energy stored in a rod or anybody which is d form that's it so the energy stored will be half y a by l into x square that's it that's the answer as simple as that so the elastic potential energy stored in any deformed body is half okay equivalent constant of spring into x square extension square equivalent spring constant is y a by l as simple as that very good now there is another way of writing the same formula and that's what i want you to see that okay let's see how we can write the other way of the same thing now remember that young's modulus correct young's modulus is stress by string and stress was force by area correct stress was forced by area and strain was x by l let's somehow use all these things probably i might get something let's try this out so why okay let's just substitute both of these things over here so i'll get young's modulus is force um and then we get uh by area and change in length upon original length i think i have y a and l below over here okay let's do one thing so y a x divided by l is f wow very good so y a by l into x is f so here is what i'll do u is half okay y a x divided by l i've just taken it aside and one of the x is separate fair enough but i know one more thing this force divided by area is stress this y a x by l divided by area is stress so if i divide this with area i know in the next step if i divide this with area i am going to get stress but to maintain and preserve the equality i have to multiply by area i have to multiply by area correct one last thing if i divide x with original length i get strain x by l is strain so to preserve the equality i need to multiply it by l fair enough now see what happens in the next step it will become half this thing is force by area force by area is nothing but stress x by l is nothing but strain area into length what do you think is this come on my over here so what is area of cross section into length isn't this volume as simple as that so can i just say stressed into strain into volume interesting right that's a very interesting formula this potential energy is half stress into stream into volume as simple as that thank you unforgettable love yeah so some books also write energy per unit volume is half stressed into strain that's also fine energy per unit volume is half stress into strain yeah it's the same thing so this and this both formulas you should remember okay this is easy k is y a by l if you remember that it's very easy this is also very easy half stress into strain into volume is total energy so one and the same thing so i put that formula just for you energy density it is called what is this term called it's called energy density so it is in joules per meter cube we can notice the unit this is energy per unit volume it's also called as energy density how much energy is there per unit volume perfect excellent let's go ahead shall we do some questions based on this okay there we go now there's a beautiful simulation of elastic energy look at this there is a rubber band there are two matchsticks you can try it at home with parental supervision yeah you stretch that rubber band you pull that rubber band leave it from one matchstick there is elastic energy stored in it that matchstick goes and hits that matchstick that's it it produces heat sparks energy so where did that heat energy come from it has come from you know that sparks that ignition has come from the elastic energy what a beautiful way of showing elastical energy interesting okay energy conversion from elastic to sparks and then heat and light and all of that let's do some questions here you have it there is a steel wire of 1.5 meter length area of cross section 1.5 millimeter square it is stretched by 1.5 centimeters then what is the work done per unit volume let's see if you can solve this question within a minute not more than a minute okay i'm giving you one minute yes it got sheared off over there yeah that was there let's see how many if we can do this come on come on bachelor yes uh you can try it out home but with supervision don't try it alone because it can be dangerous yes all right yeah yeah the matchsticks are sure but the rubber band was longitudinal high moles looks like you are late ok 25 seconds to go figure this out the wires length is given area of cross section is given extension is given young's modulus is given work done per unit volume means the energy stored per unit volume as simple as that come on let's do this hardly 10 seconds to go come on my warriors i know few things are not given but you can rearrange the terms and you can still get it and the time [Music] is up let's do this this work done per unit volume just means energy density which is half stress into string but stress is not given strain can be calculated because x is given change in length and original length stress is not given but i can do one small trick young's modulus is stress by strain therefore stresses young's modulus into stream young's modulus is given so how about putting that over here so this will be half instead of sigma put it as young's modulus into strain into the stream so this will become half young's modulus strain square correct so now start solving half young's modulus is 2 into 10 to the power 11 strain change in length which is 1.5 centimeters so 1.5 to 10 to the power minus 2 this is whole square okay upon original length original length is 1.5 meters you can see so many things will get cancelled this to this to 1.5 1.5 fair enough so what do we get 10 to the power 11 into 10 to the power minus 2 whole square is 10 to the power minus 4 11 minus 4 that's 7 right so 10 to the power 7 so is it there yep it is that's the answer unit wise it is joules per meter cube because this is energy density very good so j roop the questions could be similar for mains and nate but still i would say it is a 70 to 80 percent match 70 percent of the questions will match but those 30 questions will be slightly higher than j means okay the 20 30 percent approx all right cool very good that's the answer i hope many of you got it next question coming up on your screen two wires of the same diameter same material the length r l and two l force is also same ratio of the work done in the two wires will be not work done per unit volume just the total work done very interesting let's try to understand and decipher what is given two hours of the same diameter the meaning of same diameter means same area of cross section the meaning of same material means same young's modulus okay same young's modulus because material property decides young's modulus lengths are different forces are also same so f is basically also same so the question is work done work done is basically the energy stored elastic energy so let's try to see if there is a formula for that what can we do think work done which is energy i think i can use half into you know stress into strain into volume well i can do that or i can probably somehow rearrange it in some different form like it was half k into x square k is nothing but this yeah k is nothing but y a by l remember that was the equivalent spring constant into x square now let's see what else can we do oh there x is not given x could be different because lengths are different can i do something about it because x could be different right so how about using another trick up my sleeve so y is force by area by change in length upon original length if you realign this equation which is y is f by ax into l rearrange it further so x comes on the top it will become f l by a y interesting so i know what is x x is f l by a y put it over here and see what happens will become half y a by l x square so f square l square by a square y square see what an all gets cancelled 1y gets cancelled one of the area gets cancelled one of the lengths gets cancelled so i am just left with half f square into l by a y out of these terms observe f is constant f is same same diameter same area area is same same material same young's modulus so can you quickly observe potential energy stored is directly proportional to the length potential energy stored is directly proportional to the length and this energy was nothing but the work done i've just mentioned it so basically the work done is proportional to the length so hence w 1 by w 2 will be l 1 by l 2 what is the lens ratio lengths are l and 2 l so therefore it will be l and 2 l that means 1 by 2 hence the answer will be option a done done very good verma looks like you're quick very good arun even no it's not d unfortunately yes it is option a so beautiful application of energy concept and the definition which was there young's modulus you have to just play around with it that's all hello kaneska welcome welcome join in all the new warriors in case you have missed the class and you forgot that the class is there or you're very new to the channel first of all hit the subscribe button join the only english medium channel in the country for engineering entrance cable and friends board preparation everything on this channel the only english medium channel for all the english medium students go ahead join them okay now there's a beautiful curve that we are going to see stress and strain curve beautiful okay it's amazing to notice it now imagine okay i don't have anything to break maybe but yes i think i have found something that i can break and i'm going to show that to you [Music] wow i have a almost worn out rubber band can you see it i don't know yeah let's see this is almost like elastic but still it shows some plastic property beyond a point stress stream curve stress is what i apply force per unit area strain is the deformation so force per unit area on one side and the effect which is the stream the deformation on the other side i don't know this is also for icse board because all the boards have the same portion obviously everybody is studying newton's laws everybody is studying uh you know rotation everybody is telling the same things it's not different it's just the boards are different and the manner in which they cover the syllabus is different but at the end of the day you are studying the same thing okay don't spam by the way now what i'm going to do is i'm going to apply some force if i apply stress what is happening my warriors if i apply stress what is happening strain is increasing or decreasing come on let me know in the chat box come on my warriors if i apply stress strain is increasing or decreasing and is the stress proportional to the strain yes or no come on more stress more strain more stress more strain right now if i leave the stress it comes back to its original shape i apply stress deformation more strain leave the stress strain goes off so as stress increases strain increases as stress relieves or goes away strain also goes away more stress more strain no stress no strain comes back perfect now i keep stretching it i think beyond the point if i stretch it i will stretch it oh my god now i leave it i think the length has increased i don't know whether we can see it the length has increased i can feel it oh my god it even broke after a point if i keep stretching it oh my god this broke i don't know whether you can see it and if i leave it now now you have a longer rubber band now you have a longer rubber band okay you have a longer rubber band yeah so what has happened beyond the point when you sleep stretching it it becomes plastic in nature it shows more plasticky behavior when you stretch till the limit then it comes back but if you put so much force but don't allow it to break and you leave it it will deform permanently it shows plasticky behavior so that point that point till which it shows elastic behavior and after the point when it converts into plastic that point is called that point is called yield stress or yield point what is it called yield point y-i-e-l-d yield point so what is yield point after real point the elastic behavior converts into plastic behavior no unfair technical love this is not my wife's hair band okay she doesn't use this this bad i mean i get pretty decent salary i think i can afford a much better hair bands i'm not touching my wife's yeah makeup kit yeah this is a hairband which was there in my draw for some reason i just found it in my stationery drawer okay great okay cello if i use this kind of hairbands for my wife i'm pretty sure she's going to run away all right cool now if i apply more force let's break this oh there it goes it breaks stuck breaking point so every material has its breaking point we have two things over here you can see that it just broke perfect so that is what the stress strain curve is i just showed you practically how stress strain curve looks like by demonstration and now we are going to actually see it on this board so you pull it pull it pull it it becomes weak and it finally breaks so if you look at the graph let me show it to you right over here see pull pull pull pull tuck break this is how the stress strain graph looks like in this region do you see in this region the stress increases strain increases do you see this point what is this called yield stress what is yield stress this maximum stress till which it will show elastic behavior beyond this point if you go this is plastic zone what is this plastic zone from b to c if you leave it it will be deformed if you leave it it will be deformed perfect and do you see there is a maximum limit till which it can go that maximum limit is ultimate strength it is the strength of that material is the strength of that material look at that strength of that material that's it after that point it breaks also notice this graph has a slope what do you think the slope will represent what do you think the slope will represent come on my warriors what do you think the slope will represent for this graph i am going to pause it at the right moment okay yep there we go there we have it yeah tan theta all right so we have the breaking stress right over here okay first of all let me mark some zones this is called as the elastic zone this is called as the plastic zone this is where it breaks the slope believe me the slope is yeah what is this stress right stress by strain height by base what is stress by screen it is young's modulus so the slope will give you young's modulus very good chandan no problem unforgettable love it's okay yeah it's always fun i'm not your very strict teacher who is going to come with a stick and hit you with that stick okay we are all here to have fun and learn okay so the slope gives you stress by strain which is young's modulus perfect now some more things even before this point even before this point there is another point let me call it i don't know maybe x point or i don't know something else you can call it there is a point before which you know the curve can become curved as well this graph can become curved it might show some kind of non-linear behavior if it shows non-linear behavior in the elastic zone then this is also called as the proportional proportional limit and hooke's law is only applicable in this zone so in this zone where it is proportional when stress is proportional to the strain only there hooke's law is obeyed so understand the difference between proportional limit and elastic limit in proportional limit stress is proportional to strain from this point to this point it is still elastic but it is not proportional understand yes abhirami it is exactly for class 11 be it cbse be it icse be g be ignate yes you can attend it so understand the difference between these points last thing over here is if you calculate the area under the graph let's see what it will be this is stress height wise base wise it is strain what is the area of that graph the area the area will be half base into height does it ring a bell ring a bell jagdeep there is no point brooding over the past you have one more term to work you have internals to work on and you your other papers even if the marks decreases in one it will increase in the other if you work but if you stay depressed and you cry over the past then it will not okay so watch my motivational video which i just conducted one hour back on this channel strategy for physics watch it properly you will feel motivated so what do you think it is this is nothing but energy density so this is nothing but energy per unit volume that's what it will give you very good excellent day excellent very good now the last thing over here is sometimes you will see the graph going up like this they will show you arrow marks arrow marks means are you increasing the stress or decreasing the stress if it is this way you are basically increasing it if it is this way you are basically decreasing the stress from this point to this point because what is this point b this is basically your elastic limit this is your elastic limit right the limit till which it stays elastic in nature so if you remove the stress it is going to come back here but by chance for example in this plastic zone if you go till this point let's have a choose a point here and you remove it so understand it's not a two-way it will increase till this point but if you try to decrease it will not come via the same path in fact it will go somewhere here this is how it behaves so if you increase till this point and leave it it will come here if you increase it till here and leave it it might come over here that's how it will look like what this means look at this here there is no stress but there is strain look at that bottom most point there is no stress but it has deformed meaning it has deformed permanently it has deformed permanently when you relieve it it comes back here but not to the same shape and size it has got permanently deformed so this is also called as permanent permanent set because it has permanently set itself to a new shape and size understood yeah hope to see you jagdeep tomorrow at 11 o'clock i'm going to conduct a class hello simple girl hello muthuram welcome aboard so that's what you should know about stress and strain graphs let's see some beautiful questions on it but i have already put up all the theory a is the basically proportional limit till which hooke's law is obeyed b is the point till which material remains elastic it's also called as yield point and the maximum point till which it can bear the strength or tensile strength beyond this it breaks okay so that's what it is very good so what does this depend on this depends on the material okay whether it is aluminium whether it is this that it depends on that so some students ask sir more young's modulus sir so it has more stress sorry more breaking strength that is wrong see let me tell you one thing just because a material has more young's modulus does not mean it has higher strength imagine it is also possible another graph which has less slope but it goes like this look at this look at this this is material b and this is material a amongst these two material red and black answer this question whose young's modulus is more young's modulus of a are young's modulus of b whose young's modulus is more okay this is a straight line i hope you can see that straight line till here and then it becomes good whose young's modulus is more come on quickly answer this question b or a obviously more slow who has higher slope a has higher slope the red graph has higher slope look at this the red graph the red graph slope is higher so the red graph that means a so it's just based on the concept of slope understood this yeah many students make a mistake over here if i ask you the strength the strength of a versus the strength the strength of b now whose strength is higher yes jagdeep it is it is yeah from a to b hooke's law is not obeyed right uh from a to b uh it is obeyed uh only till proportional limit okay so now the gap between proportional limit and elastic limit is usually very small okay now a strength is less you can see that this graph ends over here b strength is more the strength of b is more so understand the difference be very careful so the strength of the graph should be seen here look at this b has bigger strength because it breaks later so where does it break so these are two different things how many of you understood this concept young's modulus is different from the strength of the material strength of the material has got nothing to do with young's modulus you can see the inequalities are different everybody got it please put up a yo please put up a thumbs up in the chat box let's do questions now okay the breaking stress of the wire depends on quickly answer this question it's not inversely proportional duction it could be same it could be more anna i'm saying they are not related that's one definitely definitely okay the breaking stress of the wire depends on c very good material of the wire perfect proud of you looks like you are very attentive during the class yeah it does not depend on radius it depends on the material so aluminium has different strength steel has different strength copper has different strength very good if you have a experiment and the load basically the stress and or basically the force you can say this is the force and there are four wires same material same length but different area which is the thickest wire let's see come on how many of you can solve this question within few seconds it's not very difficult i'll give you some hints same material means same young's modulus same length that means original length areas are different and load load means force extension or elongation means x try to think how was the formula young's modulus was forced by area extension by length let's write it again so f by a and l goes on the top x over here so i think force versus elongation is us so f will be y a by l into x now basically it's force versus x graph force versus x graph y is same and the length is same so you can see over here this term over here is nothing but the slope of force versus x graph who has the highest slope who has the highest slope a has the max slope if a has the max slope that means area is also maximum so the question is which is the thickest wire done simple got it perfect so let's move ahead next question to break a wire of 1 meter length minimum 40 kg weight is required then if you take a wire of the same material but double the radius then if the length is 6 meters how much is the breaking weight very interesting question let's see how many of you can do this what should be the new breaking weight required observe it's very very easy let me tell you that come on come on think think think options are here 80 240 200 160. break a wire iron says b interesting material means young's modulus is same interesting remember in the stress versus strain graph okay it was like this this is what the breaking this was what the breaking strength was here right and for a given material for a given material this graph is decided it is fixed so when the material is same not just young's modulus but even the stress versus even the stress versus oops sorry the stress versus the strain graph is same if the stress versus the strain graph is same what does it mean the breaking stress the breaking stress is also going to be same what is breaking stress breaking stress is force by area it's got nothing to do with the length so to break a wire of 1 meter length minimum of 40 kg weight is required if the wire of the same material but double the radius now this is the part doubling the radius if the radius is made two times the area of cross section will become four times why because area is pi r square so if radius becomes double area will become four times so if the denominator becomes 4 times to keep the ratio same the force should also become 4 times understood this concept is breaking stress right it is the same for a given material so denominator becomes 4 times numerator should become 4 times so 4 times of 40 how much it is 160 because this 40 kg weight will now have to be multiplied four times then done oh my god mr i hope you will watch the replays very soon okay but all the best and but make sure you watch it very good now it's time to give you the homework this is your first homework questions you're going to put up all the answers in the comment section this is your second question for homework okay beautiful question on stress strain graph a third question on homework here it is and let me show you all the students who have saw the homework last lecture so which was my last lecture last lecture was simple harmonic motion and if you have missed it you should definitely watch angular shims and pendulums it's right over here okay that was the previous class and it was the last class of shm but we'll have more sessions on shm as well even elasticity and mechanical properties we are going to have many sessions on problem solving don't worry about it very good esprit very good roshni you guys have been consistent very good dakshin very good chandan very good saja very good harita very good goku not and thank you for all the lovely comments and thank you all the lovely students who are regular and who are attending and sometimes you might not be able to put up the answers to the homework question but that's okay also remember my courses are available for you if you are a pro member for free so free free courses of streaser okay sir for all the we pro students so if you're a vpro student then it is absolutely free of cost for 11th standard so for 11th standard what are the courses number one derivation scores all the derivations of 11th standard it will be helpful for you second hc verma short answer course you will see that third numerical problem solving numerical courses also number four error of problem solving if you search for this on your phone on your tab or on your laptop enroll more you will get it all these courses not just mine but also so many other teachers courses are just available for you so you can 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Channel: Vedantu JEE English

Views: 59,517

Keywords: mechanical properties of solid, mechanical properties of solid class 11, physics mechanical properties of solids, mechanical properties of solid jee, mechanical properties, mechanical properties of solids class 11 notes, elasticity in physics, elasticity class 11, elasticity physics class 11, stress strain curves, stress strain diagram, stress strain graph, elasticity modulus, jee physics, jee main, jee 2023, vedantu jee enthuse english, online classes, shreyas sir vedantu

Id: trFlo2n0I2c

Length: 110min 29sec (6629 seconds)

Published: Mon Dec 06 2021