In an adiabatic process, the relationship between temperature and volume is given by T1 × V1^(γ-1) = T2 × V2^(γ-1), where γ is the adiabatic index. For a gas with γ = 1.5, initial volume V1 = 800 cm³, initial temperature T1 = 300 K, and final volume V2 = 200 cm³, the final temperature T2 = T1 × (V1/V2)^(γ-1) = 300 × (800/200)^(0.5) = 300 × 2 = 600 K. The change in temperature is 600 - 300 = 300 K.
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RE-NEET 2026 Top 100 Physics MCQs 🔥 Score Booster Session追加:
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Let's start today's session. In this session, we'll try to complete 100 MCQ questions. These are going to be a mix of your entire syllabus. Right?
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A we are going to complete top 100 MCQ questions. Right.
Let's start with the first question which is somewhat like this. This is our first problem. This is from JW mains 2025 and it is from thermodynamics. All right. Let's read this problem. Question says a gas kept in a container having four having walls which are thermally insulated which are thermally non-conducting. Initially gas has a volume of Initially gas has a volume of 800 cm per cube and temperature of 27°C.
We are going to convert it into Kelvin.
It will become 300 kel. The change in temperature when the gas is adiabetically adiabatically compressed to 200 cm per cube. We have to find out that temperature my dear friends. Right?
Clear question is all sorted. They have also given you that because uh they have also given you that gamma for this gas is 1.5.
Gamma for this gas is 1.5. And now we have to quickly start this problem. My dear friends, be a little quick. Attempt it. Attempt this question. Then I'm going to explain.
And in the meantime, let me also know if everything is clear. Be quick. Be quick my dear friends.
Come on. We have to find out the final temperature. Right? In these types of problem, first of all understand that they are saying that this this is an this process is adiabatic.
That means it is compressed adiabatically. Now we know the equation of adiabetic process. It is P V raised to the power gamma is equals to constant. This is the equation my dear friends. P V raised to the power gamma. This is the equation that we have to look for. Right? If you are going to use this equation those you can also say that sir instead of PV we can always write PV= to NRT. Right? We can always write PV is equals to NRT. If instead of pressure because we don't want pressure we can write down NRT divided by V. Or you can also simply remember it. So instead of pressure we can write down temperature. We can write down temperature and we can write down volume raised to the power gamma minus1 is equals to constant.
So hopefully you all remember this equation. If you have any doubt quickly write down this equation. This is known as equ uh you you we have also seen many polyropic processes right. So this is for adiabetic TV raised to the power gamma. Gamma is given instead of p I can write down nrt divided by v. That means v raised to the power gamma minus 1 and I have got temperature nr will be of course constant. So this is also constant. This basically means my dear friends now I can say that t_sub_1 v_sub_1 raised to the power gamma -1 is equals to tsub2 v_sub_2 raised to the power gamma minus 1. Right? I need to find out tsub2. So I'll write ts2 equals to t_sub_1 and v_sub_1 divided by v_sub_2 raised to the power gamma - 1.
Now t1 is I believe 27°C. I can simply write it as 300 kel 273 + 27. So this will become 300.
Volume v1 was initial volume was 800.
Finally the volume we have compressed it to 200 raised to the power gamma. Gamma is 3x2 or 1.5 - 1 right this will become 4 this will become 300 * 4 raised to the power 1 by 2 that means our final temperature will become 300 * 2 that is 600 kel hopefully first question is absolutely clear to all of you clear right everything's fine Quickly let me know in the chat box.
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Be a little quick, my dear friends.
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Is everything fine?
Done.
Can I move on to the next one?
Can I move on to the next one my dear friends? a similar type of a problem those but now in this question they are not saying that it is an adiabetic compression or expansion right they are saying that we have they have given a a a gen a random equation PV raised to the power 3x2 PV raised to the power 3x2 please understand that this this basically means that we are talking about PV raised to the power some some value a and that is equals to constant Now again they are saying you have to calculate the work done. If you are going to listen to me I'll simply say that please remember the formula for work done for a polyropic process also.
It will save a lot of time right? If you don't want to do that then see there are two ways to solve this equation. There are two ways my dear friends to solve this equation. First way is to we know that work done can be actually written as integral of P do DV. Let me explain you the the normal method, right? P into DV.
This can be written as P dot DV and from V_sub_1 to V_sub_2. Hopefully, this is all clear to you. Right? Now, instead of this equation, instead of pressure, I can rewrite this thing as pressure can be written as K divided by V R to the power minus 3x2.
I can rewrite instead of pressure I can rewrite it as K divided by volume raised to the power 3x2. I'm so sorry this is + 3x2. If I want to write it in minus I can write it in with K in numerator.
Right? So instead of pressure my dear friends let me write it as k v ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra ra raised to the power minus 3x2 do dv and from v_sub_1 to v_sub_2 from v_sub_1 to v_sub_2 from v_sub_1 to v_sub_2 hopefully this makes complete sense to you right now let's simply integrate it so we are going to get k we are going to apply power rule so v ra to the power - 3x2 + 1 divided by - 3x x 2 + 1 and then we are going to have v_sub_1 and we are going to have v_sub_2 we are going to have v_sub_1 and we are going to have v_sub_2 and finally we are getting k uh my dear friends hopefully you can see that minus 3x2 this will become minus 1x2 yes everyone can see this - 3x2 + 1 it will become basically - 1.5 + 1 so it will become - 1 by 2 so - 1x2 I can rewrite this thing as -2 2k right and then instead of and then we are going to have vis the power minus 1x2 over here as well right so v minus uh sorry v ra the power minus 1x2 so I'm going to get v_sub_2 raised ^ - 1x2 minus v_sub_1 raised to the power minus 1x2 hopefully this also makes complete sense now after this step my dear friends most of students actually face slight trouble over here instead of k you can again use that equation equation. Okay. Again you can use that equation. Kindly see over here instead of K I can rewrite this thing as P1 V1 raised to the power 3x2 also I can instead of K also I can write down P2 V2 raised to the power 3x2 right now why I'm saying something like this because in the option I can see easily that I have got also pressure in my answer P1 right. So from there you can get to know that okay fine we'll have to rewrite the value of K in terms of pressure and volume. So now let's multiply it my dear friends. So you are going to get you are going to get and now if you'll allow me this minus and this minus sign will become plus. So I'll get 2 k and I've got v_sub1 raised to the power minus 1x2 that means root v_sub_1 and then I'll write minus 2 k under root v_sub_2. Now instead of k I can write down instead of k my dear friends because I have got v_sub_1 so let me use this equation.
So 2 p1 and then v_sub_1 raised to the power 3x2 and instead of v this is v_sub_1 raised to the power 1x2 and then I have got again minus2. Now in now for this k I'm going to use this equation.
Why? Because I have got v_sub_2 over here. Right? I've got v_sub_2 over here.
Although it makes no difference even if I want to rewrite this equation it will make no difference but it is a way of writing answers right so instead of k my dear friends now I'm going to write p2 * v_sub_2 raised to the power 3x2 and again uh please note that instead of we have got also one more v_sub_2 over here that is v_sub_2 raised to the power 1x2 right so this will become I can take out two common if you'll say this will become 3x2 2 + 1x 2 that is 4x2 right and that uh that is basically hopefully this makes complete sense let me just see uh uh uh uh uh yes absolutely everything is uh that is minus I'm so sorry this was actually minus my dear friends right there is a one mistake this was this was minus so let me write down minus 1x2 over here please check we have got a minus sign over here right so over there also we are going to write minus so this will be also minus and this will also be minus so I'm going to get 3x 3 - 1 that is 2 so I'm going to simply get 2 p1 v1 minus 2 p2 v_sub_2 or let's take 2 common and p1 v1 minus p2 v2 this is what you are going to get so 2 p1 v1 minus P2 V2. Now let me know in the chat box if you have any doubt else I will move on my dear friends. Clear?
Hopefully everything is sorted. Be quick.
Be quick my dear friends.
Any more doubt?
Any more doubt?
Is everything clear?
Right.
Be quick. Another method. You want to know another method?
I can also say another method. Prem by the way. Hi buddy. Long time no see. If you remember uh my dear friend there there was a formula for work done which said P2 V2 minus P1 V_sub1 divided by 1 minus and then we have got like for example as we used to write gamma if you remember for adiabetic processes right so in this case we have got instead of gamma we have got 3x2 so this will actually become p2 v_sub_2 minus p1 v_sub_1 raised to the power this will become - 1 by 2 so that means -1 and I can write down two over here this minus sign uh will change the sign of numerator we'll get 2 p1 v1 minus p2 v2 but uh so this is obviously you're going to say sir why why are you not explaining this method right huh that's what I have done uh I have missed one doubt so I that's what I have also done right you can directly use this formula also but my objective is also So to explain you the entire concept. So I have explained that if any time you want to use this basic formula fundamental formula you can always use it. Hopefully there is no doubt with this question.
Right? Can I move on? Can I give you a slightly different problem now? Let's quickly see a next question.
I think there is a a a bit of mistake in the option. So I'm going to also uh I'm going to first of all I'm going to explain this to you. This is basically instead of 1x4 I think we'll get four.
But now I'll give you uh time for this question. Let's read it. The question says and see today's class is not only about thermodynamics. We we are going to cover all chapters. Sir first please ask questions from modern physics. This is not possible. I cannot I cannot I cannot uh I cannot do this. I mean just because you want to do modern physics we cannot change the entire PPT but definitely let me tell you eco your whatever your name is we are going to definitely solve modern physics also in today's class semiconductor modern physics wave optics all the chapters right all the chapters so do not worry do not worry this is the uh this is next question the pressure P1 and density D1 we are talking about density D1 of a diatomic gas gamma is 7x5 please be prepared if They are not going to tell you gamma. Be prepared.
Right? In whenever you are solving questions in practice, this is your responsibility that whatever information is given in the question. If it is a general equation, general information like for example is gamma for this question, remember it. Try to remember it. Obviously, you all remember the value of gamma for each and everything.
But I'm just I'm just using this as example. In any other question if they are giving you some value like for example is refractive index of water is 4x3 sometimes they might not give it right let's come back so now they are talking about density they are talking about density they are saying that we need to find out it is changes suddenly the pressure changes suddenly to P2 which is greater than P1 by the way right you are going to get the PDF my dear friend do not worry and D2 we are talking about density during an adiabetic process so they have also said this is an adiabetic process. So whenever it is an adiabetic process my dear friends I think now you can quickly write it down that if it is an adiabetic process that means PV raised to the power gamma sorry PV raised to the power gamma will be constant will be constant and then they are saying the temperature of the gas increases and becomes dash times of its initial temperature given that d2 upon d1 is 32 given that d2 upon dub1 is 32 right so although this question is not at all difficult let me explain this to you if you want to give it a try please be a little quick then I will move on all right I also want you guys to solve these questions with me then I'm going to explain everything right by the way this is the adiabetic equation this is the adiabetic equation one hint One hint my dear friends of course density which is which they are say which they have said it as is d1 density can be written as mass of the gas which is which will be constant divided by volume.
So if mass is constant this will mean that density is inversely proportional to volume. Of course definitely isn't it definitely. And we can also we can also see that pressure is increasing so volume will decrease.
So if volume will decrease density will increase and that's why d2 upon d1 is 32. This is also they have given this information right. What I'm trying to say is that instead of volume you can write down density which basically means that I can rewrite this equation as pressure raised to the power sorry pressure into density raised to the power minus gamma will be constant. Can you please write down in the chat box if this equation is absolutely clear to all of you? If this equation is absolutely clear although they are not talking about pressure in this question. So again you'll have to rewrite the equation so that we can have density and we can have temperature. We can have density and we can have temperature. Is it clear?
No problem eco. If you have not revised the heat unit, no problem. Just wait for some time. We are going to solve all questions. We are going to solve all questions my dear friend. Do not worry.
First of all quickly let me know in the chat box if this is all clear to you. Is everything sorted right? Hopefully everything is sorted. Now again the next thing is my dear friend that we all know that PV equals to NRT is always possible and even if you have not revised this chapter I'm explaining in such a way that everyone will understand it.
Everyone will understand it. This is always valid for for an ideal gas.
always valid my dear friends. Do not get confused sir. They are saying PV raised to the power gamma. That is an equation of the process right? This is an equation of ideal gas. So this is always valid. This is always valid my dear friends. So from this equation those from this equation I think you we all can write instead of pressure I can write it down as n rt divided by volume right and my dear friends that that means instead of pressure I can write down temperature divided by volume.
temperature divided by volume and one upon volume can be written as density.
Please kindly see I'm not skipping any step so that you'll understand each and everything.
Again one upon volume can be written as density. So this will become t d raised to the power 1 because of this and minus gamma and that is equals to constant.
This is my final equation. And that's it my dear friends. Now after this all you need to do is you need to simply write okay fine sir that means t_1 d1 raised ^ 1 - gamma is equals to ts2 d2 raised to the power 1 - gamma raised to ^ 1 - gamma and we need to find out t2 don't forget we need to find out actually t2 upon t1 right because how many times it has increased so that means we need to find out ts2 upon t_1 so we are going to bring this t1 over here and we'll get sorry we'll get D1 upon D2 we'll get D1 upon D2 1 minus gamma and by the way D2 upon D1 is 32 so this will become 1 upon 32 and gamma they have also given us gamma that is 7 x 5 so this will become 1 - 7 x 5 so obviously I'll have a negative sign over here so I'll get 1x 32 raised to the power and this will become minus 2x x 5 - 2x 5 U hopefully you don't mind I keep on writing in one equation only right and this will now this will become 32 raised to the power 2x 5 and we all know 32 32 raised to the power 1x 5 is nothing but 2 isn't it so that means we'll get 2 raised to the power 2 so that means four so t2 is t2 upon t1 S4. So that's what I was saying that they are saying that the temperature of the gas increases and becomes dash time.
So it becomes four times. It becomes four times. Yes, that's what I was saying 1x4 can't be the correct answer.
Correct answer is going to be four.
Right? I have said it in the first part only. Is everything clear? Sorted.
Quickly let me know in the chat box. Be quick. Now I'm going to move on to different chapters also. Again we'll come back to uh thermodynamics and almost every other chapter. Okay, clear come on let me know please don't click on any link which is given. Obviously you guys are conscious about all of these things right? Ignore such spams. Okay, ch let's start let's start my dear friends let's continue to solve some more problems right yes next chapter another chapter right eco what is your name buddy so that I can address you directly so that I can address you directly let's solve this question let's solve this question when a spring is elongated by 2 cm it stored potential energy is e if the spring is elongated by additional 2 cm very basic type of a problem sir Hindi may see I I I can I can easily speak in Hindi but this is this is a PW neat English channel right so that is why I'm speaking in English clear uh when a spring is elongated by 2 cm my dear friends when a spring is elongated by 2 cm the stored potential energy is E you need to pay attention into these things right hi Sadhart we are very nice name buddy very nice name my elder brother's name is also If the spring is elongated by additional 2 cm, what will be the increase in its potential energy? Great. So we all know kindly see we all know that potential energy which is written as E actually can be written as 1 upon 2 kx² 1 upon 2 kx². Now they are saying if we are going if we are actually elongating it by 2 cm. So square of 2 cm this would mean four. Let's just keep it like this.
Let's just keep it like this. Now we need to find out new energy such that we have we have stretched it by additional 2 cm. Kindly note additional 2 cm.
Right? So initial elongation will be will still be there. Right? Initial elongation will still be there. So we are going to write half k. Now your new elongation becomes 2 + 2 that is four.
So square of four. Now we can easily rewrite it. Rewrite it as half k * 4 and multiplied by 4. So now see how easy it is. This was actually e. So this simply becomes four * of e. Please do not assume that sir why are you explaining these questions? These are very simple.
We know that energy is directly dependent on x you if you're going to increase it by 2 cm more. We can simply write it write it as four times of initial. My point is I should explain it in such a way that everyone can understand right everyone should understand the solution. All right. My name is Subrat. My name is Subrat. Okay.
Ch. Now let's move on to the next question. Hopefully this is all clear.
Although uh this is a pro this is again from thermodynamics. So if you guys are feeling a little bored. I'm not going to explain it entirely. I can give it to you as a homework. The question this is the equation. My dear friends, this is the equation, right? So I can rewrite this equation as this is an a polyropic equation. I can rewrite this equation as P V raised to the power - 1 by 2 is equals to K. Now you can solve it. Is it clear? Now you can easily solve it. Is that fine? Because over here we have got root V on the other side. So I I I I have to write it with with pressure. So if I'm going to rewrite this thing with pressure, it will become PV raised to the power minus 1x2. And now please solve it as a homework. Right? So all along this lecture, I'm going to give you some very good questions in homework. Right? So please solve them after my class and you are going to get the PDF of this. Yes. Uh Sadhart if if your if your name is Sadhart buddy gamma is not minus 1 by 2. Now over here we are going to call it as a polyotropic constant. Gamma is gamma R. Gamma is CP by CV. H gamma is CP by CV. So if you have got diatomic gas, gamma is different. We have got poly triatomic gas gamma is different. This is not gamma. This is a polyotropic constant.
We don't have only four processes. There can be infinitely many processes. So for those infinitely many processes, we can have infinitely many equations and that this constant is known as polyotropic constant. Clear? Let's move on.
Uh that is why I have said that generally the formula is integral of P do DV for work done. Consider a system consisting of a central solid sphere.
Let me help you with the diagram. We have got a central solid sphere. My dear friends, something like this, right? And it has got mass m and mass m and radius r. It is surrounded by a concentric It is surrounded by a concentric spherical shell of mass 2mm. Right? So kindly note this. This question it's a nice problem but easy or whenever I say nice I I don't mean to say it is difficult. Right? It's an interesting question. See this has mass 2m and radius of this sphere is 3R. Radius of this sphere is 3R and then radius of the smaller sphere is is R I believe and mass is M. So mass is M and this radius is R. And then they are saying that determine the net gravitational force. Determine the net gravitational force experienced by a particle of mass m located at a radial distance of 2 R. located at a radial distance of 2 R from the common center.
That means from the common center my dear friends we need to go to a distance of 2 R which will be somewhere over here which will be somewhere over here. So this is the distance of 2 R and we are keeping a mass small M over here and we have to find out the net force.
Clear is quotient all sorted my dear friends be quick. Is quot question all sorted? Now see we have done electric electro u elastic potential energy now gravitation then thermodynamics we have a mix of all questions right what is going to be the force very very good very good sanker very good sadhart very good see my dear friends okay hold on now some some tips time whenever you are going to get a question from gravitation you can solve it with the concepts of electro rostatics also if you have any problem in electrostatics if you remember if we have got a shell over here kindly see huh what I'm trying to say everybody please listen this is a shell so we know the gravitational field inside the shell will be zero just like electric field intensity inside the shell is zero all right Sanjana very good just like okay hi shushi hi just like electric field intensity inside a spherical conducting shell is zero. Similarly, if I have got a mass spherical shell which has got mass m, there will be no mass inside it.
So there will be no gravitational field intensity. So there will be no force experienced by small m due to this due to this spherical shell. So easy. And I can assume the entire mass of this solid sphere to be at this point. Please, please, please listen to me very carefully. Only when the point where we are trying to find out the gravitational field intensity is is is outside from the surface. Right? So this point is outside for this solid sphere. So I can assume the entire mass is at capital M.
That means the force on small M becomes G M1 M_sub_2 divided by square of distance. And this is so simple.
Right? And exactly like exactly like electrostatics, isn't it? Write down in the chat box. This is exactly like electrostatics. So very easy. Now we can move on. If you have any doubt, do let me know in the chat box. I will answer it. Hi Tarun. Hello. Hello. Hi. Good evening. Hi Dan. Good evening. Hi Vashita. Good evening. Good evening.
Good evening.
Hi. Hi. Hello. Hello. Hello. Hello.
Hello. You have spammed me, right?
Hello. Ch. Now let's move on to the next problem.
Fluid. Next question is from fluid, right? Next question is from fluid. Next question says, a vessel is filled with three immissible liquids. Immissible means immissible basically means that these are not going to get mixed. Of densities row, two row and three row.
Okay. So there is a typo over here. Let me write it for you. and three row from the top to bottom. So obviously we can see that row two row three row. Now they are saying that each liquid forms a layer of height h. We can see see that ignoring the atmospheric pressure. This is very important. Ignoring the atmospheric pressure. So you don't have to worry about atmospheric pressure. Now they are saying what is the ratio of fluid pressure at the interface between the top and the middle liquids that is point A to the pressure at the interface between the middle and the bottom that is point B.
This is also easy, not at all difficult, right? But language is is slightly confusing. Slightly not very but slightly confusing, right? If you're going to allow me, my dear friends, the pressure at point P can be written as pressure at point sorry, pressure at point A, not P. Pressure at point A can be written as atmospheric pressure plus row G into H. And instead of density, I have written row. But they are saying that kindly ignore the atmospheric pressure. So let me ignore it. So this becomes ro gh this becomes ro gh and pressure at b will become pressure at b will become now at b please remember that this liquid will also apply the pressure and this liquid will also apply the pressure. So there will be pressure due to surface uh due to liquid liquid uh this liquid right and plus 2 row g into h that is 3 row g into h so the ratio will become p a by pb will become 1x3 that's what they were saying 1x3 done yes very Good. Very good. Very good. Very good.
Good.
All right. So, if you think all of these questions are easy, let me give you another problem which is slightly moderate. Slight slightly moderate.
Right. You have to imagine this question. You have to imagine the diagram. Okay. And if you want, I can also give you this question in pool. S why one question from different chapters? Why not 10 questions from one chapter? But then you will get then see then you let me tell you this is a very interesting uh point we must what we are trying to do is hold on hold on Sat let me explain why we are doing this see all along this week I have completed chyntatics so in that particular class I have only solved the question from chyntatics then Newton laws of motion and work per energy then we have done rotational motion and center of mass now it is a time to solve mixed questions Shock your mind. Now, shock your brain.
If you're going, if your brain knows after this also thermodynamics will come, after this also thermodynamics will come, you will not be able to shock your brain, which is what happens in your final neat exam. So, after every after revision after uh after revision of particular chapters, please solve mix questions so that you can be you you can get ready for your final need exam.
Clear? So let's start 90 seconds or 90 seconds will be sufficient. Let's start.
Come on be quick.
Shall I start?
Poll is running. Huh? Poll is running.
You can give your answers in the chat box. My dear friends, question is saying we have got a current carrying loop. So this is a loop. It has got total 200 turns radius of 3 cm and an orientation in the it lies in the xy plane. Lies in the xy plane basically means lies in the xy plane basically means of course this is y this is x and this is your plane.
Now they are saying and centered at origin. So this is origin of course if a current of 2 ampere flows fine 2 a force what is the magnet what is the magnetic field strength at this point. Now this point is on the Z axis. This is on the of course it is on the Z axis. That means we'll have to use the formula of magnetic field due to a current carrying circular coil at a point on the axis. At a point on the axis and by that formula is something like this. Please remember mu not upon 4 pi. Simply write mu not upon 4 pi. Then write total number of turns. Then write 2 pi r².
Then write current whole divided by whole divided by r² that is square of radius + x² raised to the power 3x2 raised to the power 3x2. Now if I'm going to solve this equation for you although I believe after writing the formula you must be able to solve it. Mu not upon 4 pi can be written as 10 ^ minus 7 multiplied by number of turns are 200. So 200 multiplied by 2 multiplied by 2 pi. So uh they are giving answer in pi. So I don't have to worry about this. And r² my dear friends radius so radius will square of radius will become 9 and I have to also convert it into meter. So 10 ^ -4 so u and this will become me²ared right so 9 into 10 ^ -4 and multiplied by 3 that is current is 3 a I believe current is oh I'm so sorry current is 2 a current is 2 a divided by again square of again square of r and if you if you again see please see this is three right this is square of three let it be in centimeter. Let it be in cm. This is four square of three and square of four.
And if you if you are going to take root, it will become it will become five. So that means this is square. This is 5 cube and then you'll have also cm cube that means 10 ^ - 6. Is everything clear? Right? Everything sorted. Quickly write down in the chat box if you have if you have understood what I have done over here.
Right? This is 3 square 4 square triplet 3 4 5. So this is 5 squared. So this root get cancels out and I have got a cube over here. So this is 5 cube and this is by the way this is cm raised to the power cube. Finally it is centime raised to the power cube. That is five 5 cube and cm cube. So 1 cm is 10 ^ -2. So this becomes 10 ^ - 6. If you are going to solve it I have solved it personally.
I think your correct answer was either A or either or B. Let me check. Answer.
You will get your answer. No doubt about it my dear friends. Do not worry. The answer is uh the answer is one. The answer is one. Absolutely.
No doubt about it. You will get it.
You'll get the answer. Answer is one. A.
Very good. Good. Good. Good. Great. Good to all of you.
Any more doubt? Can I move on to the next question? Right.
This was a moderate level problem. The calculation made it moderate. Other than the calculation concept if if they are going to only if you are going to ask me sir what about concept? If only the concept is concerned question was easy.
Now let's move on to another question right and my dear friends another question is let's suppose this a crate is placed on the horizontal bed of a truck so you have got a you have got a horizontal bed of a truck so let's say this is the horizontal bed of a truck right and just to make this look like a truck let's say these are the wheels that's it right and then we have got a crate over Here we have got a crate over here. Then they are saying determine the maximum acceleration of this. Determine the maximum acceleration of the truck that can have without the crate sliding.
Without the crate sliding. Without the crate sliding.
Come on.
This is what we need to find out. Be quick.
This is what we need to find out. We need to find out the maximum acceleration of the truck that can have without the crate sliding.
In all of these types of problem, please remember if this if this uh if this truck bed is going to move, there will be a friction force that will act that will try to which will try to move this crate also with this bed. So that relative motion can be so so that we can resist the relative motion not we the friction force can resist the relative motion right and the value of this friction force will be my dear friends please see value of this friction force will be mu * of n this is going to be the value of friction force so the maximum acceleration of the of the crate can be maximum acceleration of the crate can be simply mu * g So mu was 0.4 and g is 10. So that means this can move with 4 m/s squared of acceleration. This crate can have can maximum it can move with 4 m/s squared. Now if they are saying that it must not slip. If they are saying that it must not slide that means that truck if truck has a maximum acceleration of four then friction will be sufficient enough kindly understand the concept then friction will be sufficient enough to move this to hold this crate with respect to the with the truck and if it is going to move with more acceleration then kinetic friction will start to act and it will it will start to slide.
Right? So answer is easy. Option four is the absolutely the correct one. Quickly write down in the chat box if everything's clear. Right? Do not get worried that they have not given us mass. Mass is not required. All right.
Quickly write down in the chat box. Be quick.
Some of you have said D. So D is not correct. Answer is going to be 4 m/s squared. Answer is going to be 4 m/s squared. Is it clear? Quickly write down in the chat box. Any more doubts.
Can I move on to the next one?
Be quick.
Next problem. This is also a nice question. My dear friends, this is also a nice question.
From mechanical properties from mechanical properties of solid a uniform steel cable 10 m long with a cross-sectional area of 1 cm square is suspended from a ceiling. Determine the elongation due to the cable's own weight.
Use density of steel as row 8,000 kg per meter cube. Youngs modulus is also given and g is also given. Do it by yourself.
Do it by yourself. Don't take any help.
This is for your own good my dear friends. You can see the level of these question is absolutely comparable to what NTA can ask. Right? You can judge this. So let's let's do it honestly without any distraction. Let's all let's all complete this these questions.
Option A. Okay. Okay. Let me check. I'll check for you my dear friend if option A is correct or not.
Well, I don't have the answer for this.
I don't have we we'll have to solve this.
The elongation is basically mg l / 2 a y.
This is the formula that we'll use. If you'll ask me, I can derive it for you.
If you'll ask me, I can derive it for you. But first of all, let's check the answer. We don't have mass right now, right? So to find out the mass, we'll have to multiply density with volume.
So density is 8,000.
Volume is area multiplied by area is 1 cm². That means 1 into 10 ^ - 4 and length is 10 m.
Right? Length is 10 m. So these four zeros will get cancelled out and I'll get 8 kg.
I'll get 8 kg. So this will become 80 nton multiplied by 10 m whole divided by 2.
Area is 1 cm²ared. So 10 ^ -4 and young's modulus is 2 into 10 ^ 11. 2 into 10 ^ 11. My dear friends, this will become four and this will become 20.
Hopefully you guys can see right. This thing will become uh se uh 7 and I'll get 200 * 10 ^ - 7 or I can rewrite this thing as 2 into 10 ^ - 5 m. If I want to write it in millimeter, so I'll get 0.02 into 10 ^ -3 m or 0.02 mm.
0.02 mm.
So option A is certainly the correct answer. Very very good. Now let me tell you one thing. Many times students commit one mistake in this question. Let me explain that to you. This is the formula. This is a different formula.
Kindly note down and remember this formula. This is elongation.
This is elongation due to selfweight of the rod. elongation due to due to self selfweight of the of the rod, right? Why? Because sometimes you might get confused with the normal derivation. For example, as if let's suppose we have got two types of cases. We have got two cases over here.
In first case we have got a block which is kept like this of 8 kg of 8 kg and let's say the original length is L and we know that this is mg and Young's modulus of this is Y area of cross-section is A. So you are going to say you're going to say to me sir Y is actually equals to force upon area time change in length this is what you want us to find out time L. So delta x will be instead of f you're going to write mg l divided by a into y. Are you are you getting it? Are you getting it what I'm trying to say? So this is this is the case when this is the case when when string is massless when string is massless.
when string is massless right this is the case when string is massless in this case we have got a rod and rod has its own mass rod has its own mass so in this particular case we cannot say that 80 nton is acting at this point we cannot say that so what we'll have to do we'll have to integrate it I I'm explaining it again I'm that's what that that's what I'm I'm trying to say this is a nice problem right what I'm trying to say is if you have any doubt please ask me pointed out. I'll definitely explain.
Right? All right. I I'll definitely explain. See, what I'm trying to say is that we have got two types of cases in these in these types of problems. Over here, we we don't have mass in this string, but this string can extend.
There can be an extension, right? So, this the entire force is acting at this point. The entire force is acting at this point. But over here, we cannot say something like that. So what we are going to do is we are going to use integration to derive the formula.
So this is formula is mgl divided by 2 a y and over here I'm sorry over here we have got formula is mgl divided by 2 a y. Now let me give you one homework for your practice and then I'll move on to the next question. In this part my dear friend what we are going to do is we are going to go to a distance of x. See I'm I'm explaining you the entire derivation without wasting your time so that you can really understand this is let's suppose that we are going at a distance of x and we are selecting a length of dx let's say this is a this is dx right so this length will be total length is l so this will become l minus x what is going to be the mass of this length so mass of this part of the length will be the entire mass is mire length is L. So this is linear mass density multiplied by this length. So this will become you this will become the new length. I'm sorry this will become the new mass. It means that over here mg is not acting but what is acting?
We are having a force of m by l * l - x * g. And then let's find out the extension in this infinitely small element.
Are you getting it what I'm trying to say? Right. So when you are going to do it, you are going to do it like this.
Let's suppose you are writing it as dx dash. This is extension in this dx. This is extension in this dx. And then you will try to integrate it. Is everything clear my dear friend? And when you are going to integrate it, you will land up to this answer. You'll land up to this answer. From where to where you will have to integrate? from x =0 to x = to l. If you are if you are from any of my batch be it power batch or yakinit English you can refer to your notes I have derived it for you right I have derived it for you now let's move on to the next question right let's move on to the next question let me give you another problem let's solve this question one question from electrostatics come on let's start Be quick. Two point charges +2 microum and minus 8 microoum are placed 15 cm apart on the line connecting the two charges. Identify the locations where the net potential net electric potential is zero. Question is very simple but you need to understand that you can have two points unlike electric field. Unlike the case of electric field you can have two points. Can you please quickly write down in the chat box if everything was clear from the last last topic last question?
Jitendra Mthali.
Come on, answer me first. Everything's clear. Can we move on to the next problem?
So you have to find out the point where net potential will become zero. You have to find out the point where the net potential will will become zero.
Definitely one of the point will be in between of these two and point will be nearer to the smaller charge. So let's suppose this is point P this is X. So this will become 15 - X.
So potential at point P will become K Q / X is equals to K Q / 15 - X. K can be cancelled out. This will become 4. That means 15 - X is equ= to 4X. That means x will be equals to 3 cm.
X will be equals to 3 cm. Clear? X will be equals to 3 cm. Right? Next question.
Next part is this same point can be somewhere over here also nearer to the smaller charge. You can't say sir why not over there? Because there is no possibility because this is larger in magnitude. This is larger in magnitude which means that the next point will be somewhere over here. Let's call it as Pdash. Let's call this distance is X. So that means this distance will become 15 + X. And then again solve it. You're going to get your answer as minus 5. Why? Because this point is at origin. This point is at origin.
Hopefully this makes complete sense.
Right? Any more doubt my dear friends?
Can we move on to the next question?
quickly let me know we we have to be a little quick so that we can solve maximum questions with maximum possible explanation right maximum possible explanation come on let's be a little quick so this question is very easy this question is very easy so I'm not going to waste a lot of time in this they are saying that if a not is the bhar radius for the ground state of a of a hydrogen atom right of a hydrogen atom determine the radius of the orbit for an electron in the second excited state of berilium. Can you please help me with the atomic number of berilium? Well, I know that second excited state basically means that they are talking about n equals to 3. And when they are talking about berilium, can I write it as four?
Hydrogen, helium, lithium, berilium.
Right? Clear? So this is going to become four.
And then you can write down And then you can write down RN equals to AN N² by Z.
Be quick my dear friends. Be a little quick. Let me know the correct answer.
Is it clear? So n is going to be 9. N is three. So this will become 9 a divided by 4. 9 a / 4.
This was very easy.
Let's solve this question. This is a nice problem. This is a nice problem.
Let me make some stars over here. Come on. Let's start this question. Let's solve it together. Let's solve it together.
Question is saying a particle of mass small m travels along the positive x-axis. This is uh towards the origin with a speed of 8 m/s. Another particle of mass 2m travels along the positive y-axis towards the origin with a speed of 2 m/s. They are set to collide. They are set to collide at the origin. The center of mass of this two particle system. Center of mass of this two particle system will travel along which straight line will travel along which straight line. Come on let's do this problem my dear friends. Starting the poll 60 seconds let's start.
Come on be quick.
Come on.
Well, if you are good in class 12th physics, that's very very good. So, you have got sufficient amount of time to improve your class 11th also, right?
Everybody is getting option B. Very good here. Very good. If you guys are able to solve this question then fine. Your preparation is in right track. Do not do not become a rabbit. Keep on studying.
Right? Do not get any more lenient.
But very good. If you can solve this question, very good. Why I'm saying this? Please understand. See, let's understand it conceptually, right? They are they are set to collide at this point. Clear? They are set to collide at this point. Fine. Can I I know that collision is basically my dear friends collision is basically an it is because of internal forces. There are no external forces involved. There are no external forces involved.
There are no external forces involved.
Right? So that means center of mass will keep on move. It will keep on moving in the in the same direction. So let's find out the velocity of center of mass. So this this will be m into 8 icap m/s plus 2m into 2 m/s jcap whole divided by uh m + 2 m that is 3 m. Obviously I can cancel out m and I'll get 8x3 icap plus 4x3 jcap. Now this basically means that at this point the center of mass at at origin center of mass has velocity 8x3 icap and 4x3 jcap. Please see huh please see this is 8x3 m/s along x-axis and we have got 4x3 m/s along yaxis. Clear? This means that the resultant will be obviously will be bended towards 8x3 something like this.
Let's say this is the direction in which center of mass is moving. This is the velocity of center of mass. When we are going to find out the resultant of these two we are going to get let's find out the slope of this of this vector. Clear?
Let's find out the slope of this vector theta. So when you are going to find out tan theta you're going to say so tan theta will be obviously perpendicular that is 4x3 divided by base and base is 8x3 this gets cancels out this gets cancels out we we'll have 1x2 we'll have 1x2 that means we have to look for a for an equation of straight line which has got slope of 1x2 which has got slope of slope of 1 by 2 which is this option B and most of you were saying option B right or option A. Can you please write down what you guys were constantly saying whether it was option B or option A? I forgot.
You guys were constantly saying option B or option A. Quickly let me know in the chat box and please see this is a nice problem.
This is a nice problem my dear friends.
After this I'm going to move on to the next question. Correct answer is option B.
Very good. Very very very good. Great.
All right. Let's solve this question.
This is an assertion reasoning question.
60 seconds will be more than sufficient.
60 seconds will be more than sufficient.
Let's start. Assertion says a ladder leaning against a smooth vertical wall cannot remain in equilibrium if the force is also smooth. Sir notes PDF notes PDF. You'll get the PDF of these notes on PWN neat English WhatsApp channel. And where are you going to find that channel? in the the link will be in the description box. After this live stream is over, you will get it. All right. Come on. I think assertion is absolutely correct. I think assertion is absolutely correct. And reason says for equilibrium the net horizontal force on the ladder must be zero. The normal force from the vertical force is horizontal and only a frictional force from the floor can counteract can counteract it. This is absolutely clear.
Very very nice explanation. Both A and R are true and R is the correct explanation for assertion. C option is absolutely correct.
C option is absolutely correct.
Well, some of you have said A is false.
Some of you have said A is false. In that case, let me explain this problem to you. My dear friends, what's going to happen is let's draw let's draw some usual forces, usual suspects. Mg will act downward.
Kindly see here mg will act downward.
Yes sir. Normal reaction will act in this direction due to due to floor.
Normal reaction will act in this direction due to wall. Right? Now the thing is obviously you can say sir we have got no problem. This is normal reaction. This is normal reaction from the floor and this will get balanced by Ng right. And this is normal reaction from the wall. From where are you going to balance this normal reaction from the wall? It has to be balanced with a frictional force which will which will act in this direction which will act in this direction. This is friction force provided by the floor.
And kindly remember that whenever somebody is saying to you that a system or a or anything is in equilibrium, this basically means that they are saying that summation of force forces along all the axises XYZ should be zero and net torque about all points should be zero.
And if you remember in neat 2025 also they have asked a similar question. They have asked a numerical questions based on this concept. Right? So please note it down. Is everything clear? No more doubts. Can I move on to the next question? If you're going to write down yes in the chat box, I'll also feel good and I'll be I that will reassure me that everything is going fine. Quickly write down in the chat box. Then I'm moving on.
Then I'm moving on. My dear friends, I think it's not necessary that I'll ex I'll completely explain all the questions. Like for example is this one.
Like for example is this one. My dear friends, they are saying you have to find out the ratio of root mean square speed. Ratio of root mean square speed is V RMS. And we know that V RMS is nothing but 3 RT by molecular mass.
So this means that V RMS is directly proportional to V RMS is directly proportional to roo<unk> of T by M. That's it. Now uh square of helium helium atom capital m is 4 and for sulfur dioxide writing is 64 32 + 32 it is 64 so I think you can do it now clear is it sorted quickly write down in the chat box be quick yes can we move on to the next problem let's solve this question let's solve this problem and I'm going to give you poll in this one be quick Be quick. Be quick. Consider the branch of a circuit shown from point P to point Q. The current is at a particular moment and is decreasing at a rate of 10 ^ 4 ampere per second. Decreasing at the rate of 10 ^ 4 ampere per second. Come on, be quick.
Be quick my dear friends.
Come on. Come on. Come on. Come on. Come on.
Are you saying C for this?
Are you saying C for this?
Okay, let's check.
Let's see.
By the way, current is decreasing. Huh?
If current is decreasing then you can imagine that we have got a battery over here which is supporting the current and it has got emf ldi by dt. L is l is I believe 2 m a m 2 mh henry and gi by g ch is 10 to the power 4. So this means that this is nothing but this is 20 volt and we need to move in this direction.
So how we are going to write down? We are going to write down potential of point P. My dear friends, whenever you move in direction of current and you pass through a resistance, there is always a potential drop. There is always a potential drop. So that means 5 * 2 is 10. I'll write it with a negative sign because there's a potential drop. Now you're moving from negative potential to positive potential. That means potential gain plus 20 volt. Then again you are moving from negative to positive plus 20 volt. Then again you are moving from a uh from a resistance that means 5 * 4 is again 20 and is equals to VQ my dear friends I think I can cancel out this 20 and VP minus VQ is coming out to be plus I'm sorry minus 10 but they are not asking this they are asking VQ minus VP so anyway your answer was wrong it is not C it is actually D it is Three.
Sir, one number is wrong. What one number? What one number? Can you please uh Shubham Shoubham Gotham? Sir, what?
Which one number buddy? Which one number? Hi Henry. Hi.
One number is wrong. I mean the first question is wrong or one number is wrong? What? What do you mean? Five twos are 10. Everything is correct here. Huh?
Sir sir 120 plus marks please guide me sir question solve okay I'll guide you just wait a second but I don't think anything is wrong take kindly check quickly let me know in the chat box this is absolutely correct D is absolutely correct What has happened? I forgot to take VQ minus VQ minus VP. Still if you have forgot to take VQ minus VP and you have taken VP minus VQ, you should get minus 10 as answer. Now, how come you are saying sir one number is wrong a number?
Be quick.
Be really really quick.
Come on, everything's clear. Even if you have mistakenly taken it as VP minus VQ, your answer should have come minus 10, right? Your answer should come minus 10.
Clear?
Come on. Which one is wrong? I don't think any answer is wrong till here. I don't think so. And if you're saying number one, what was number one?
Everything is correct here. Number one to definitely it is correct. Pura, I have derived it. There's no doubt. There is no doubt. Please don't waste your teacher's time here.
Come on, let's do this question.
Come on, be quick. Clear, let's start.
In a in a YDSC light with a wavelength of 500 Newton meter is used, wavelength of 500 Newton meter is used.
The intensity of a light at a point on the screen is found to be 25% of the maximum possible intensity.
What is the minimum non zero What is the minimum nonzero path difference between the waves?
What is what is the minimum nonzero path difference? All right. All right, UI.
Thank you. Thank you, buddy. Thank you for appreciating this. Ch let's let me explain this to you. See in a YDAC experiment right let me explain you the entire concept in a YDAC experiment we know that we have got two coherent sources that means that net intensity can be written as the general formula is po I not cos² phase difference is five. So we are going to write it as 5 by2. Now they are saying my dear friends kindly note now they are saying that instead of net intensity we are getting 25% of maximum intensity. So maximum intensity is this.
So 25% of maximum intensity is going to be simply I not. So I not = to 4 I cos² 5 by2 I not and I not can be cancelled out.
cos² by2 will become 1x4.
After this I can rewrite cos 5x2 as 1x 2.
If cos 5 by2 is 1 by 2, this means that 5 by2 will be<unk> by2 my dear friends cos gives 1 by 2 at 60°. So this will become this will become 120° my dear friends. This will this is actually<unk> by3 and this means that phase difference will become 2<unk> by3 120° and now use the relation between use the relation between path difference and phase difference. Path difference is remember it like this. If you have got delta x you'll have lambda over here divided by 2 pi multiplied by phase difference. This is the formula.
So you're going to get lambda upon 2 pi and by the way let me now write down lambda because they have given me the value of lambda which is 500 nanometer 500 nanome multiplied by delta 5 is 2 p<unk> by 3 is 2 pi by 3 divided by 2 pi so 2 pi and 2 pi will get will get canceled out 500 divided by 3 here 500 divided by 3 is what 500 divided by 3 will be 160 6 166.666 666 66 66 66 66 66 66 66 66 66 66 666 666 666 and so on. So 167 option B is absolutely correct. Got it? Everything is clear. Everything is clear. Huh? Let me know.
Let me know my dear friends. Then I'm going to move on to the next question.
Sir, this is how you should say. This is how you should say.
Are you talking about this? Just a second.
>> Which language >> are you talking about? This question, my dear friend. Are you talking about this question? H first.
Answer.
Are you talking about this or which question? Here kindly write down the question.
Or you are talking about this.
The change in temperature when the Oh yes yes yes yes yes.
The change in temperature change in temperature is 300 kel. 300 kel. Thank you so much. I take my words back. I apologize to you. I take my words back.
I apologize to you Shubam Gotham. Very very good my dear friend. Very very very good. I am so sorry I have not paid sufficient attention to your chat.
Right.
Thank you so much. Everyone should thank you Shubhham Gotham. They have asked us the change and by mistake I have found out the final temperature only. So change is going to be change is going to be in final minus initial and that is going to be 300 kel. Thank you so much Shuba.
Apologies. Mistake accepted.
Mistake accepted. All right, no problem.
Let's move on. Let's move on, my dear friends. Let's move on. I think we have solved some pretty good level of good number of questions still here. Let's quickly move on to the next one. Okay.
All right.
Thank you. Now, let's solve this question. Okay, Shubam. Let's solve this question, my dear friend. This is from Shubam. You're from Nepal. Thank you so much, buddy. Thank you. And apologies.
Cho. Let's start. A plano convex lens. A plano A plano convex lens made up of a material with the refractive index 1.75.
Okay. 1.75 has a radius of curvature 15 cm from the curved surface. All right. If the plain surface of the lens is silvered, this is a nice problem. This is a nice problem.
Please understand what is the effective focal length of the resulting mirror system. I'm going to give you some time till please solve this. Till then I'm going to explain it also. See what they are trying to say is what they are trying to say is that you have got a plano con convex lens sorry you have got a plano convex convex lens something like this right something like this. So this is the radius of curvature of this part is infinity.
Radius of curvature of this is is I believe 15 cm. And after this they are silvering it. H after this they are silvering it. But first of all let's find out the focal length of this lens.
So one upon focal length of lens will become refractive index of lens divided by refractive index of surrounding medium that is air. So I don't have to write it down. Mul -1 1 upon r1 - 1 upon r2.
So we we are going to get uh let me just simply write it over here. You're going to see this is 1.75 minus 1 that is 0.75. you're going to get 0.75 and then you have got uh 1 upon r 1 upon r that is 15 and minus one upon infinity that is zero. So so so so please solve this equation. Be quickly solve this uh uh uh find me the answer.
Come on me the answer for this one my dear friend. What is the focal length?
What is the focal length? Answer should be I think it should be five. That's what I'm getting. Answer should be five. You know, it is finally coming out as five.
It is finally coming out as five, my dear friends. Right. It is finally coming out as five. Please check.
5 cm.
It is finally coming out as 5 cm. I mean right now we have not solved it entirely. I'm simply telling you the focal length of length. Right? And now the equivalent the most important thing is if you're going to silver it then the formula will become 1 upon f equivalent is equals to 1 upon focal length of mirror minus 2 * divided 2 divided by focal length of lens. You have you must remember this.
This is very important and this is what makes this question important and I believe my dear friends uh uh anything else this was 20 h just a second let's See a this is 20. I sorry this is 20.
This is 20. Please do the calculation again. This is 20 cm. That means this is 1 upon 10. That means this is going to be 10 cm. Option B is absolutely correct my dear friends. Option B is absolutely correct. Please see please see it one one more time. Yes.
Yes. Yes. Sorry.
Huh? Take it. Done. Clear.
Formula was absolutely fine.
Formula was absolutely fine.
Any more doubt?
Let me check also.
Is there any mistake? H Clear.
Clear.
Please check this again here.
Answer is absolutely correct. But let's check this again. This is going to become 0.75 and divided by 15. Please check this again. Answer is absolutely clear.
Answer is absolutely correct. Yes, question is definitely of nice level.
Definitely. A certain amount of ideal gas is enclosed in a cylinder. Okay.
Certain amount of ideal gas is enclosed in a cylinder. If 150 calorie of heat is provided to the system.
All right. 150 calorie of heat is provided to the system and simultaneously 30 joule of work is performed.
Okay. Take 30 joule of work is performed on the system. What is the resultant change in internal energy? The important thing is that you have to convert one calorie into jewel. You have to convert 1 calorie into jewel. So that means please use delta q is equals to delta w plus delta u. So if you're supplying energy, if you're supplying heat, we are going to take it as positive. We are going to take it as positive. That means this will become 150 * 4.2 equals to and work is performed on the system. If work is performed on the system, on the system basically means negative.
On the system basically means negative.
And this is minus30.
So what is the change in internal energy? What is this my dear friends? Uh 05 and this is this is six this is 600 now is it so right?
Mhm.
Hm.
Delta UV will be greater than 600 that is 660. Come on be quick my dear friends be quick. 630 + 600 + 30 660 June is the correct answer for this one.
Clear? This question is also clear.
All right. Clear my dear friends.
Not 630 660 is the correct answer.
Kindly note it down. This is 15 * 42 is is going to be 6 630.
That is what you you might be doing wrong.
Yes. 630. This is 630. This is minus 30.
This will become 660. Please understand work is performed on the system.
Negative heat is supplied to the system.
Positive. So this is positive. This is negative. When this will go over here, this will become positive. And 660 is the correct answer. Right? Clear? Done.
Can I move on to the next question? This is also a very nice problem. Very very very nice problem.
Nice question.
Okay, let's solve this question also.
A body of mass 3M is launched with an initial velocity V with an initial velocity V at an angle of theta to the horizontal. At the peak of its trajectory, at the peak of its trajectory, it explodes into two fragments of mass 2 M and M. All right? into mass 2 M and M. 2M momentarily stops and falls vertically.
Determine the speed of the lighter fragment capital M just before it strikes the ground.
Clear? Is everything sorted?
All right.
Be quick.
Come on. Huh? To that was I think plano concave was 20. Now huh? That's what I've said 20. It was coming out to be I think 0.05 after getting cancelled out if I'm not wrong. That was coming out to be 1 upon 0.05 something like this right buddy? So this will become 100 and that will become 20. Correct? Not five but it will become 20. That's what you are you are saying now this will become the 0.05 right and that is one upon L that is one upon L so L will become 1 upon 0.05 05 that means 100 divided by 5 that is 20.
So 20 over here. Clear right? Done.
Be quick. Sorted.
Come on. Be quick. This question is clear. This question is clear. Now let's solve this question. This is also a nice problem as you can read it.
Shall I solve it for you?
Let's see. Hopefully you all all have now read it.
In this problem, see what's going to happen is at this particular point it it actually explodes.
At this point it explodes.
Usually in the questions of explosion we use the concept of center of mass. Over here things are slightly different. Let me tell you how. My dear friends, just before the collision, please see just before the collision, the entire momentum will be written something like this. This velocity will be V cos theta.
Why so? Because at this point, the horizontal component of velocity is V cos theta. The horizontal component of velocity is V cos theta. So this will remain same. So this is before explosion. Please see. Huh? This is before explosion.
This is before explosion. Now after explosion what happens is let me use another pen another color. After explosion the the mass 2m momentarily stops and fall vertically vertically. So 2m falls over here.
Right? And the another mass that is m it will move with some different velocity.
Let's say that is vdash.
Let's say that is Vdash. Please hear me out very carefully. This question is very good and I'm going to explain each and every doubt related with this question. No worries. So we are going to first of all we know that whenever we'll have a explosion questions we are going to use conservation of linear momentum.
Conservation of linear momentum. So conservation of linear momentum says before collision the total mass was 3 m.
The total mass was 3 m.
velocity was v cos theta and after collision 2m momentarily comes to rest and the smaller mass will move with a velocity of let's say v or vdash let's say it moves with a velocity of vdash right and this becomes zero m can be canceled out with this that means vdash is equals to 3 E cos theta.
Now kindly see please see this particle will come like this. This the smaller particle will come like this.
My dear friends the vertical velocity of this particle will be will remain same. I mean the magnitude will remain same. This was v sin theta. So this velocity should also be v sin theta. Let me know in the chat box and please think about it. A very very nice problem. Think about it. Why?
Because it is coming coming to the ground from the same height. I'm explaining the reason also. As the particle particle comes to ground particle comes to ground from same height comes to ground from from same height same height. So initial velocity was v sin theta in vertical direction. It used this velocity and its final velocity became zero at the highest point. Now whatever is the velocity in the x direction when it is going to fall back to the ground it will attain the same magnitude of velocity.
This is going to be v sin theta and the x component will not change. And now the new x component is mind you it is vdash.
It is vdash.
So that means the final velocity will be final velo and they they are actually talking about uh determine the speed. So final speed will be under root of v sin theta². So v² sin² theta plus vdash² and vdash² is this. So it will become 9 v² cos² theta my dear friend 1 v² sin square theta and v² cos² theta will become 1 right that means v² so we'll get under root of v² + 8 v² cos² theta v square can be t taken out as common and we'll be we'll be left with option a v 1 + 8 cos² theta Right answer.
Even if you are going to now I'll take the now now I'll take your doubts.
Sadhart is saying sir 2m can have velocity under root 2 gh. So if you're going to do that you will get to the same answer bu because this is this is h right. So the particle used v sin theta to get to h.
So this under root 2 gh will also be v sin theta. Now is that correct? Please don't get worried about with with this vdash. I am simply saying I am simply saying the basic concept of motion under gravity. I am saying if you're going to throw a particle with a velocity of v sin theta and it will go at the top and when it will come back at this point speed will remain v sin theta.
So at this point when collision happens x velocity changes and when this particle falls because it falls from the same height it will it will attain the same magnitude of velocity in negative direction v sin theta.
Very nice problem. Is it clear?
Right.
Any more doubt?
Sh. Now let's move on to the next question.
Next question is this.
Be quick.
Next question is this. A concave mirror with a focal length. A concave mirror with a focal length of 30 cm is oriented such that its principal axis aligns with the line y = to 4x3x 4x 3x.
A point object is situated at the origin 0. So point object is at this point 0.
If the pole of the mirror's mirror is 90 cm, this is 90 cm away from the origin along the principal axis. Determine the coordinates of the resulting image.
Determine the coordinates of the resulting image. Let's find out the resulting image. Please note that object is at this point. Please note my dear friends. And point object is at the origin. So this is where the point object is 0 comma 0 comma 0.
Come on, be quick.
Solve. Solve. My dear friends, solve. And let me know if you have any doubt.
First of all, this is a normal concave mirror.
So I'm going to simply say 1 upon focal length is equals to 1 upon v minus 1 upon u.
Which means that 1 upon v will be 1 upon 90 - 1 upon 30 * 3 * 3. So this will become v will become - 455 cm.
V will become - 455 cm. That means somewhere over here.
This is going to be V.
This distance is this distance is 45 cm.
This distance is 45 cm.
Right? And if you want to find out the coordinates, my dear friends, please note that this is going to be the y-coordinate and this is going to be the x coordinate. And looking at this equation, we can see that tan theta is equals to slope and that is equals to 4x3. This means that theta is equals to 53°.
So this angle is 53°.
This angle is 53°.
This angle is 53°.
And if this angle is 53° and let's say this is Y and let's say this is X, then I can simply say that sin 53° sin 53° which is which will be equals to 4x 5 and that will be equals to y divided by hypotenus that is 45. This will become 9 and y will become 36 cm.
So there is only one 36 cm. That means option a is correct. Now you can also use cos 53. cos 53° will be 3x 5 and that will be equals to x divided by 45.
So this will become 9 and x will be equals to 27 cm. So x is 27 cm.
Come on, let me know in the chat box if you have any doubt. Be quick.
Clear.
Done and dusted. Any more doubt? Be quick.
Come on.
This is also a nice problem, my dear friends.
done and dusted. Can we move on?
Let's solve this question now.
Last problem was really really nice. The fundamental frequency of air column in a cylindrical pipe open at both ends is measured to be f not. Okay. So this means that if you have got a if you have got a pipe an open pipe like this the fundamental frequency we going to draw the diagram something like this. We'll have an anti-node over here. We'll have an anti-node over here.
We'll have a node over here. And this length will be actually equals to this is lambda x4 this is lambda x4 this will be lambda by 2 right. So v can be written as f into lambda that is 2l. So f can be written as v upon 2 lambda.
Right? Now they are saying the pipe is partially submerged into vertically into a liquid such that okay such that 2/3 they are saying such that 2/3 of the length is inside the liquid. So let's suppose this is the liquid.
Let's suppose this is the this is the liquid and we have submerged the this organ pipe something like this such that 23 is inside if 23 is inside that means this length will become lx3 and over here we are going to have a node so something like this will happen something like this will happen what will be the fundamental new frequency of the air column. So mind you this length will be lambda x4 and lambda by 4 will be equals to lx3 which means lambda will be 4 lx3 lambda will be 4 lx by3 clearly write down in the chat box velocity will remain same because still this is air right so v = to f dash or let me write it as fdash into f into lambda So lambda is 4 L by 3. So fdash will be 3 V by 4 L 3 V by 4 L. So uh I'm sorry. Yeah. And instead of uh Okay. So instead of lambda uh sorry you have to write down 2 L over here.
Right? So that means answer will be 3x2 of f.
You guys can see I can rewrite this thing as v / 2 l. So this will become 3 fx by 2.
Is everything clear? Quickly write down in the chat box. Nice problem.
Be quick. Any more doubts?
Let me know. Then I'll move on to the next question.
Done and dusted my dear friends.
Next is an object in simple harmonic motion has total mechanical energy total mechanical energy of 160 Jew. What is the potential energy when the displacement of the when the dis when the displacement from the mean position is half the amplitude is half the amplitude. Kindly see here those total energy is written by total energy is written by half K a² and total mechanical energy is 160 Jew right so potential energy will be half K into X² and instead of X they are saying let's write it as half of amplitude so that means a² by 4. So that means 160/ K²/ K² is is total energy. So this will become 40 Jew. This will become 40 JW.
And if somebody wants to know sir what is going to be the kinetic energy at this point. So kindly note that kinetic energy will be total energy minus potential energy. So total energy is 160, potential energy is 40. So kinetic energy will be 120 Jew.
Right.
Hopefully this is all clear.
A quotion from error. A quotient from error. The density of a material in the shape of a cylinder is to be determined. The measured values are this is mass.
This is mass and cross-sectional radius is that and length is this. Right?
Length is this. Everything's clear till here we can move on. Right? What is the maximum possible percentage error in the density measurement? My dear friends, density can be written as density can be written as mass divided by volume.
That is mass divided by if you're talking about cylinder p<unk> r² into l, right? P<unk> R² into L. This basically means that if you want to find out percentage error in density, you can rewrite this thing as delta M by M plus 2 * of deltar by R plus delta L by L in percentage form.
Okay. Right. and delta m is now please see this is these questions are very easy and they they are very also common in neat exams delta m is 0.4 you don't have to worry about the unit in these types of problems because anyway units are going to get canceled out I'm sorry delta m is not 0.4 it is 04 divided by 0.4 4 plus 2 * of deltar.
Delta R is 0.3.
Again, you don't have to worry about the unit. 0.3 divided by 0.2 and plus delta L is 0.05 and divided by 5 and multiply all of these things with 100.
Right? You can cancel out one point and this thing can be written as 0.01.
Uh you can cancel out one of the point.
This thing can this will be written as 0.03.
This will be written as 0.01. If you'll multiply 100 this will become 1% plus this will become 3% and that will become 1%. So finally your answer will be 5 percentage.
5 percentage is the correct answer.
Clear?
Quickly let me know in the chat box if you have any doubt. Be quick.
Come on.
Done.
Can we move on to the next one? My dear friends, see this problem is also nice. This question is also a nice one. Question says, a block of copper with 200 g mass.
So mass is 200 g. It is heated from 20°C to 70°C using a radiation of wavelength 3,300 angstrom.
Calculate the number of photons required to achieve this temperature change. To achieve this temperature change, they have also given you specific heat capacity. Clear? So using specific heat capacity, first of all, let's find out.
Please understand the question what they are trying to say right we are we are using electromagnetic radiation we are using the energy of photons to increase its temperature so let's first find out the energy energy required so delta Q will be or simply Q will be ms delta t q will be m s deltat t right let's first find this out then I'll explain everything mass is 200 g and this is also in gram so please note down the unit in the unit in which you are writing everything. So I'm writing it in 200 g because specific heat capacity is also in gram and I'll finally get my answer in jewel. So 0.5 joule per g per degree and delta t is 50.
So my final answer is in SI unit. Kindly note my final answer is in SI unit. I have I have written mass in gram. Why?
Because specific heat capacity was given in gram. Right? So this point will get cancelceled out. This will become two.
Finally I'll get 400 Jew. So that means total heat is 400 Jew. And we are going to get this heat from from photons.
Energy of one photon is HC by lambda. So let's suppose we have got total n number of photons. So formula of n will be total energy that is 400 multiplied by wavelength. Wavelength is 3,300 anstrom.
divided by h into c divided by h is 6.6 6 into 10 ^ - 34 * C that is 3 into 10 ^ 8. This is going to be your answer.
Clear? Quickly write down in the chat box friends. Be quick.
Any more problem? Any more doubt?
Done.
Now you guys can solve this question and I think answer is a for this one.
Let me check. Answer is 6.67 into 10 ^ -19 done right. Okay.
Very good.
Very very very good.
Clear. No doubts. question was also a decent problem. moderate level of question right ch let's move on to the next one then then I think those we can also solve this question a charged particle experiences an acceleration of a that is 3 icap minus 4 jcap m/s squared when it moves through a uniform magnetic field given by this what must be the value of y what must be the value of y so friends we Know one thing that magnetic force is actually perpendicular to velocity vector and also it is perpendicular to magnetic field.
We know this.
So using this we can also write down the acceleration produced by magnetic force will also be perpendicular to magnetic field. And if they they are perpendicular we can rewrite this thing as if I'm going to write a dob this will be also zero.
So let's do this a dob is 12 and then - 4 y there is no kc cap is equals to zero so y will be equals to 3 y will be equals to 3. Option C.
Clear.
Done.
Come on.
Done. Done. Done.
Let's move to the next question. If everything's sorted now my dear friends let's okay let's solve this question the current I in the circuit shown in figure the current I in the circuit shown in figure. Answer seems to be 3E.
Uh what 3E buddy?
Which question you are talking about?
Hm. Hopefully everything is clear till this point. Let's find out the answer for this question. You have to find out the current flowing in the circuit.
Right? Find out the current flowing in the circuit.
Huh? that we have also written three.
Now we have also written it as three right? Have I written it as 4E coming going back by that time you guys solve this question. A they are also talking over here also they are talking about increase. My bad. Here also they are talking about increase in potential energy. Right my dear friends. So increase in potential energy again again again again they are talking about increase in potential energy that means delta E. So 4 E minus E that is 3. Thank you so much. This is also increase 3 E.
Correct. This is also increase 3 E. Very good. Who has said this? Please write your name.
And the next question was somewhere over here. Yes, this is the next question.
Kindly see see this is what we call as bypassing right. So these two wires are not touching each other. So if this is point A and I don't have any resistance or any electrical uh element between point A and D this basically means that I can rename this point as A.
I can rename this point as A. Right? I can rename this point as A. Similarly, this point C can be written as B because there are no electrical instruments between point B and C. Which means that 4 ohm is connected between A and B and 6 ohm is connected between A and B. So these are in parallel combination. So R equivalent will be 6 * 4 divided by 10.
So this becomes two, this becomes five.
That means 12 x 5 ohm.
And current will be voltage divided by resistance.
So this will be 5 ampere.
This is going to be 5 ampere.
Sorted clear.
Let's solve some more questions. Right?
And then I'll give you some questions in homework also.
A custom worner caliper has a main scale with 1 mm division with 1 mm divisions.
Its warner scale consists of 20 division which perfectly aligns with 16 main scale division. All right. While measuring the thickness of a plate, the zero of the verier scale falls between the 28th mm and 29th mm. All right, clear. Great.
So my dear friends please first of all understand that least count will be one main scale division minus one verier scale division.
So one main scale division minus then they are saying that 16 main scale division coincides with 20 right. So one verier scale uh division is going to be 16 divided by 20 main scale division.
So this one is going to be uh 1x5 main scale division that is 0.2 mm 0.2 2 mm right kindly please note that you're not you you don't usually see this type of problem where they actually ask to find out which verier scale division exite exactly coincides with the main scale right they usually don't ask a question like this so now we know that finally the reading is finally the main reading is 19.2 2 mm and there are no zero error. So 19.2 mm will be equals to main scale reading and main scale reading is between 28 and 29. So main scale will be 28 mm plus verier scale reading multiplied by least count that is 0.2 mm.
So this will become uh if the finally thick this this should be 29 here this should be 29 my dear friends this is not possible this should be 29 this should be 29 so this this is going to become 1.2 mm is equals to vsr* 0.2 2 mm this will get cancelled out and zero point will get cancel out by this and this will become six so one scale reading is sixth division option A option A clear see this question is slightly new slightly new my dear friends usually you don't see problem like this no eighth eth is wrong here yeah correct answer is sixth please note correct Corct answer is sixth. Absolutely no doubt about it.
You can see no about no doubt about it my dear friends. That's absolutely correct.
Everything's clear from the last one.
Can we move on to the next question?
Please see this problem. And I'm going to start poll for this one. Please start.
A series combination consists of 10 identical cells.
10 identical cells each having emf and internal resistance R. Okay. Each having emf and internal resistance R. However, however, two of these cells are connected with reversed polarity. That means these are wrongly connected.
These are wrongly connected. Clear?
If the terminals of this combination are shortcircuited, that means connected.
What is the potential difference any across any one of the correctly connected cells?
Come on, be quick.
Be quick my dear friends.
Good.
So you have got 10 identical cells. We are not going to draw 10 but let's draw few. And then out of these some of them are also wrongly connected. Right?
Some of them are wrongly connected. So E E we know that if two of them are wrongly connected then net will become net will become so you have got a total of 10 and min -4 E that means a total of 6 E see two wrongly connected will also cancel out two correctly connected cells is it clear so if let's suppose one of them is wrongly connected then this will get this will cancel out this one So this is E. This is minus E. So this will cancel out this one. This is also wrongly connected. So this will cancel out this one. So total four got cancelled. Four got removed. So remaining six will be there. So 6E and there is no effect on R equivalent. So R equivalent remains same that is 10R.
So current will be the net current will be net emf divided by 10R that means 3 E by 5R 3 E by 5R. Now they are saying what happen if we are going to connect them if we are going to short circuit them. So short circuiting them would mean something like this. So what is the potential difference between any two uh any one cell? So one cell is something like this.
E R and let's suppose current is moving like this. So what is going to be the potential difference between these two points. So if you're going to move from this direction, let's say this is point P, this is point Q. So you're going to write VP minus current 3 E divided by 5 R multiplied by R. So this R and this R gets out plus E is equals to VQ. So, VQ minus VP uh oh sorry V uh yes you can actually write down H no problem let's solve this so this is going to become E minus 3 E by 5 so this is five this is five so you're going to get 2 E by 5 so 2 E by 5 is the correct answer option B 2 E by 5 is the correct answer clear my dear No matter how you want to write it down.
So this is obviously at greater potential. This is at lower potential.
Current flows in this direction from higher potential to lower potential from outside in the external circuit. Clear?
Everything is sorted. This is also a decent question. Not difficult, not very easy. A moderate level of problem.
Quickly let me know in the chat box if everything's clear.
Please pay attention.
Can we move on to the next one?
Let's solve a question from modern physics. Right? Although we have solved some problems uh that number of photons and many more questions and let's solve this question also. Very good. Light of wavelength lambda ejects photo electrons from a metal surface with a stopping potential of V with a stopping potential of V. When the incident wavelength is changed to 1.5 lambda so inc if incident is if the wavelength is increased stopping potential will definitely decrease. So it decreases to V by2.
You have to find out the threshold wavelength. So I'm going to help you in the equation you find out the answer.
Right? So the first equation will be first the wavelength was lambda. So HC by lambda is equals to HC by lambda KN plus stopping potential and stopping potential is V.
Right? We don't want to find out uh the value of V, right? We want to find out the value of lambda KN. Next is if you're going to change the wavelength as 1.5 that means now this becomes H C 3 lambda by 2 is equals to H C by lambda KN and plus V by 2 clear this becomes V by2 so what what I'll suggest you to do is instead of V you can substitute H C by lambda minus HC by lambda KN and substitute it over here and you'll get your answer in terms of lambda.
Be quick. Let me know in the chat box if you have any doubt. Correct answer will be three. Correct answer will be three.
Lambda KN will be equals to 3 * of lambda. If you're going to solve this, please note any doubt you can solve this question very easily.
Sorted my dear friends.
Done.
Moving on to the next one. A thin uniform wire with the total resistance with the total resistance of 18 ohm is fashioned into a circular loop. All right. So we have got a circular loop like this and then it is connected across two terminals on the loop. Fine.
such that it subend an angle of 120° at the center. So something like this.
So it subtend an angle of 120° at the center something like this. So this angle is 120°.
So if this angle is 120° this angle is going to be 240°.
If this if this resistance is let's say R1 this resistance will be R2 and we know that resistance is directly dependent on length and length is directly dependent on arc length is directly dependent on theta.
So R1 will be 2 * of R2.
That means also R1 + 2 * of sorry R1 + R2 is also equals to 18.
So R1 can be written as 2 * of R2. So this is 3 * of R2 is equals to 18. So this becomes six.
I'm so sorry.
This will become 12 and this will become six.
Right? I I mean to say R2 will become 2 * of R1.
Clear? And that means finally R equivalent will be 6 into 12 divided by 18. So 3 and 4. So finally the answer will be 4 ohm.
Sorted quickly. Let me know in the chat box.
Done.
Done. Everything's clear.
Be quick.
Any more doubt?
Any more doubt my dear friends? Can we move on to the next question?
C crystal clear. Everything is sorted.
Very good.
I think we have done this question in the last class.
I think we have done this question. Huh?
Let's not repeat it all over again. In the last class uh of 500 MCQ, we have done this question in the combined class. But if you have any doubt, let me just write it down for you that force can be written as minus du by dx. F_sub_x can be written as minus du by dx and f_sub_y can be written as minus du by du dy.
Partial differentiating it. Right? So we have done this problem clear and what about this one for the wave shown in figure write the equation of this wave its profile is captured at t= to0 that means we have got a snapshot of this right we have got a snapshot of this all right so in this question wave is moving towards positive x-axis is so positive x-axis. So this will be wrong.
This can be correct. This will be wrong.
Right? Positive x-axis. And then this looks like a sign. So this is also wrong. So correct answer is B. Why?
Because obviously the function is a sign. The graph is of sign and it is moving towards positive x-axis.
It is moving towards positive x-axis.
Is it clear?
Be quick.
One question from capacitors, right? One plate of an initially uncharged parallel plate capacitor of an initially uncharged parallel plate capacitor of plate area A capital A and plate separation D and plate separation D is connected to the positive terminal of a battery of the voltage V. The negative terminal of the battery and the other plate of the capacitor are earthered as shown in the figure. Okay fine. The charge that flows from the battery, the charge that flows from the battery to the capacitor plates is please see when you are going to do something like this. This basically means that you are connecting these two points and you have got potential V. So capacitor we can write it as epsylon A by D. So charge will be Q into Q will be C * V. So C is epsylon A by D * V that's it I think nothing else epsylon A V by D nothing much right nothing much my dear friends I've got one interesting problem for you which is from uh from logic gate let's let's look at this question let's look at this question my dear friends this is a very very nice problem usually you have seen questions from this topic.
Usually you have seen easier problem from this topic, right? This is this is slightly different. Try to do it. Come on, try to do this problem.
Question is to get output one at R for the given logic gate circuit. The input values must be the input values must be this is the question. You have to find out the input values, right? And please note that we have got let me explain this question. We have got an not gate over here. So if this is X the input in this or gate will be XAR.
Then you have got X and X over here. And this is this is Y.
So this is Y. And then this is y and this is y bar. Hopefully my dear friends this is absolutely clear to you. Right friends xar n y and this is an orgate.
So this will become XAR + Y and this will become X into Y bar and a bar over there because you have got an AND gate and basically means multiply and then you have got an inverter bubble. Is everything clear? Quickly write down in the chat box. This is a nice problem. My dear friends, in this part in this type of problem, what you do is you break the line and you change the sign. So you are going to break the line. So this will become Xar + Y bar and bar. So finally this will become Xar + Y. So finally on this Q the Q will be actually equals to Xar + Y. similarly as this one.
Really nice, right? So that means R finally your R will become this is an this is a N gate again. So this will become X + Y + X + Y and a bar on it. By the way, there is no sense of writing this again and again.
See what I'm what property I'm going to use. A + A can be simply written as A.
So this thing can be simply written as Xar + Y. Now they they want us to they they are saying that to get output as one. So if this is one, this means that this should be equals to zero.
Xar + Y should be equals to zero. Now to have this as zero. Now let's check if x is zero then this will become one and if y is one so this will become one. So this is not correct. If x is 1 then this will become zero xar will become zero and if y is 1 then this will become one. So this is not correct. If x is one if x is one so xar will become zero and if y is zero then this will become zero. So this is the correct answer. If x is zero, this will be also not correct because if x is zero, xar will become one. So c is the correct answer. Really nice question. Is it clear my dear friends? See, I have also explained the drogley theorem that I have used. Everything sorted quickly write down in the chat box. Be quick from units and dimension till logic gates. I've tried my best to cover most of the topics, right? And this is a very nice problem.
Any more doubts? Now you are going to get this PDF. Now you're going to get this PDF on PWNET WhatsApp channel. PWN neat English WhatsApp channel. And you're going to get more such questions for your practice. All right? For your practice. kindly solve them various problems right so in that way we can complete these if you're going to complete these 100 questions out of these 100 I think almost 50% we have solved it in the class right now complete these complete this PDF this will be more than sufficient more than sufficient I'm talking about the level of the questions this level is more than sufficient for you now what you need to do is you need to solve some more mock exams if your if your uh syllabus is completed. If your syllabus is not completed then let me tell you I have completed till rotational motion in my next class we probably I'm going to start class 12th right and then we are going to discuss KTG and thermodynamics part after that clear so that will be all for today complete these questions see I've got various questions of different type over here right these are going to be sufficient for your practice kindly do them do these And then we'll meet in the next class my dear friends. All right. Clear?
Done.
Okay then. See you my dear friends.
Probably the next class will be on on Sunday. Okay. Bye-bye. Bye everyone.
Bye. Bye. Bye. Bye.
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