 So, let us take up another scenario, this is a very important scenario, this is called motion in a vertical circle, alright, write down, alright now do you have few examples of motion in a vertical circle, first of all what is this vertical circle, vertical circle is a circle which is moving in a plane that is vertical, okay, we define vertical with respect to accession due to gravity, fine. So, if this plane contains accession due to gravity G then this plane is vertical, fine. So, naturally if there is an object that moves in a vertical circle its potential G will change, isn't it? If you say that this is the height or this is the level where gravitation potential G is 0 then the height of the object is changing in a vertical circle, fine. So, if it is here let us say this is quarter of a circle, so this is R, yes, okay, that is correct. So, at this point if this is potential G is 0, so if this is a potential G is 0 at this location potential G will become equal to MGR, fine. So, you can see that when an object moves in a vertical circle then the potential energy of the object keeps on changing, fine. And if the object moves in a horizontal circle, fine. So, if it moves in a horizontal circle since height is not changing the potential energy of the object is not changing, fine. So, that makes the vertical circle motion a special one because here the potential energy also changes, okay. So, we can I know think of many examples quickly write down the typical examples I will talk about of course there will be many others as well. Example one, example one could be the string and mass like this. So, if you give this mass that is a mass M of velocity like this what will happen this mass will move in a vertical circle, okay. Guys, don't discuss among yourself focus, this is one of the example. So, it's a pendulum sort of thing, fine. So, pendulum actually oscillates and here you just go in a vertical circle like this, okay. So, this is example one there can be many other example I will quickly take few example two could be you know a circular track like this in which an object goes like that, fine. So, this track may not be a complete circle, fine but then it is a part of a circle. So, when this mass moves it will move in a circle like this, okay. Then third example could be a bead in a circular wire, there could be a bead like this that can move in a circular wire, fine. So, example four could be that there is a tubular passage, okay in which the mass moves getting it. So, all these are typical examples of all these are typical examples of the motion in vertical circle, okay. Meanwhile, you can please try out this particular question, I'll take two minutes. You have a mass, okay this mass is you know down vertically down like this hanging on a length L, you have given this mass a velocity which is equal to under root of 5gl. You need to find out its velocity when the mass becomes horizontal, okay. So, this is position one and that is position two. All we have to do here is to apply work in a j-thera. So, is the tension force doing any work? Tension force is not doing any work because tension is always perpendicular to the direction of motion, okay. So, this perpendicular to the motion hence work done by tension is zero and the only force that is doing work here is gravity and for that you have considered the potential energy. So, W will come out to be zero. This is equal to U2 if you assume this line to be zero gravitation potential energy. So, U2 will be equal to MG into R, K2 will be equal to half MV square minus U1 will be zero plus K1 will be equal to half M into this velocity square, okay. Let's call it as V1. So, this is half MV1 square. So, when you substitute it you will get the answer, okay. Fine. So, what I was talking about here is that in a vertical circle ultimately it is what a circular motion whether it is horizontal circle or a vertical circle ultimately it is a circular motion only and if it is a circular motion then at every moment there will be a centripetal acceleration of magnitude V square by R, fine. So, at every moment it will have an acceleration towards the center which is V square by R, fine. So, it must have a force that will create this much acceleration, fine. So, towards the center there will be a force called centripetal force that will be acting. I think we have already learned this in laws of motion chapter. I am just reiterating that make sure you are taking care of this fact that it is moving in a circle and since it is moving in a circle there will be a centripetal acceleration of magnitude V square by R towards the center, fine. And since there is a centripetal acceleration towards the center there has to be a force towards the center, getting it, right. Now, keeping all these knowledge let us try to solve this particular question. See this is not a part of theory, I am just taking a scenario and trying to tell you how you can tackle this scenario. Suppose this is mass m, it is hanging, length of the thread is l, all right. Now, if you give it a small velocity what will happen? If you give it a very small velocity it will move like this slightly this way, then it will come back that way, fine. So, it will oscillate left and right, getting it. So, if you give it a very small velocity it will just oscillate, now if I give it slightly more velocity it will be reaching horizontal level and it can swing one horizontal level to the other horizontal level, okay. Now, if I give it slightly more velocity it will reach there, okay. Now, it will reach there and suppose tension becomes zero here then what will happen? If this tension in the string at that location becomes zero then what will happen? At that moment if tension is zero what will happen to the motion of the object? Will it move in a circular motion? So, if T is zero there is absence of necessary centripetal force for it to move in a circle, fine. So, if tension becomes zero at that location then it will not move in a circle, fine. So, it will be as if an object is thrown with velocity V. So, it will become a projectile. So, it will move in a projectile way and it will not be a circular motion, getting it. So, from here to there from initial point to the point where tension becomes zero it moves in a circle and then as soon as tension becomes zero it becomes a projectile motion it no longer moves in a circle, fine. So, the necessary condition for this object to move in a circle is what tension should not become equal to zero, fine. Now, tell me where is the location where the value of tension most likely becomes zero, most likely where the tension of this mass or of this string can become zero, highest point or topmost point. So, at topmost point tension is most likely to become zero, fine. So, if T is not zero at topmost point then can I say that T will never be becoming zero, T will not be zero anywhere. Is this statement correct? If tension is not zero at the highest point then can I say that tension will not become zero anywhere. So, if tension is not zero anywhere it means that the string is not slack anywhere, string is always taut and if string is taut there is no motion along the radial direction, it is always tangential direction. So, I will say that if tension is not zero anywhere then the object will complete full circle, fine. If tension is not zero then the object will be able to complete the full circle, the mass will be just completing right down the full circle if tension tending towards zero at the topmost point, getting it? So, this mass if tension tends towards zero because tension will keep on decreasing decreasing and it will become minimum at the topmost point. So, if minimum tension itself is not zero tension will never become zero, fine. So, the limiting condition for which it will just complete the full circle is the tension at the topmost point is zero, okay. Now, listen to the question. Any doubts till now? Kindly message yes or no? You have any doubts? Kindly message? Okay, this is the last question for today then whatever is left over will take another class to finish this chapter. All of you should get the answer, okay. The question is like this, you have mass m and length l, okay. So, you need to find out what will be the minimum velocity? What should be the minimum velocity u so that this mass completes the full circle or full vertical circle? Try to do it. Clear about the question, right? I will write here. You have to find minimum velocity so that the mass completes full circle. Not correct Niranjan, don't be in a hurry, okay. Answering quickly doesn't impress me, you know that. I was joking. See, I know the thing is that if tension is just becoming zero at the topmost point then it will be able to complete the circle, fine. So, let's try to balance out the forces here. So, let's assume that at the topmost point its velocity is v, okay. So, down there will be a gravity force, let's say mg is that force and there will be a tension force like this, fine. And there will be a centimeter acceleration of magnitude v square by r which is l, radius is l, okay. So, if I write down equation there I will get t plus mg is equal to mass time acceleration, fine. So, if tension is just becoming zero at the topmost point then what will I get? I will get mg is equal to mv square by l, fine. So, mv square I will get this as equal to mgl, fine. So, let's, I will quickly write this as v square equals to gl, but this is what? This is not the initial velocity, this is the final velocity, okay. So, if final velocity square is equal to gl, okay, then tension will become zero at the topmost point. This is the minimum required final velocity that this mass should have, okay. So, minimum required final velocity will give you minimum required initial velocity, okay. Now, I am going to write down work energy theorem between this point and that point. So, w is equal to, in case you have any doubt please keep messaging u2 plus k2 minus u1 plus k1. Now, is there any force other than gravity that is doing work here? You can see tension is a force, but tension is always perpendicular to the motion of the object. Motion of the object is tangent to the circle and tension is normal to the circle, fine. So, work done will be zero by the tension, okay. And gravity is doing the work, but for gravity you are anyway considering potential energy. So, work done will be zero. u2 is what? There is only gravitation potential energy, there is no spring potential energy. So, if I assume this level to be zero potential energy, then u2 will be equal to what? u2 will be equal to mg into 2L because the height of this object, second point is 2L now L and another L, okay. So, mg L plus k2. k2 is what? Half m into v square minus u1 is initial potential energy which is zero plus initial kinetic energy half m u square, okay. So, all you have to do now is to substitute the values, you will get mg 2L plus half m into v square. v square is gL finds this minus half m u square will be equal to zero. So, u will come out to be under root of 5gl. So, this is the minimum required velocity for the mass at the lower most point to complete the full circle, okay. When it is tied with a string, okay, this is the condition which you should remember because at times you can use it directly in column solving, okay. So, that is it for today and there are a few topics still left in this chapter and a lot of problem practice we need to do in this chapter to master this, okay. So, at least 200 to 300 questions you have to solve your own to master this topic, okay. And let me tell you that is not something which I am asking and nobody else is doing. Everybody who is serious is practicing lots and lots of questions, okay. So, the homework nobody has asked me any doubts from the previous homework, okay. See guys, you know, I can only tell you from my experience, okay. And I don't want you to make errors because you will not be able to learn from your errors and implement it to correct yourself because you will get only one chance, right. If you make error in that chance itself, you will not get a second chance, okay. So, make sure you do what I am saying, alright. Follow exactly what I say, nothing less, nothing more and you will be through and I am not asking something which is like beyond as in nobody else is doing. Everybody is working equally hard those who are serious. Anyways, you need to solve entire hcv on work, power, energy, okay. This is for J mains only. If you are serious about J mains, solve entire hcv on work, power, energy by next week, okay. And if you are aiming for J advanced, then I will be sending a worksheet. You message me, then I will be sending you, once you are done with this, okay. J advanced is not like you should not do this and then you start doing the advanced level questions. No, that's not how you prepare for J advanced. You have to prepare from the basic level up, okay. So, once you are done with this, message me, I will send you a worksheet of around 100 to 200 questions for J advanced, okay. J advanced is this plus a worksheet that I will be sending you once you ping me that you are done with this, all right. Okay, and those who are preparing for KVPY, those who are preparing for KVPY tomorrow will have a class 4.30pm to 7.30pm, okay. I am going to talk about, you know, system of particles, okay. This is the start of rigid body motion and that we are anyway doing it after work by energy chapter, okay. So, you don't, I mean, you are not missing anything if you are not attending the KVPY lecture, okay. So, this will be anyway doing towards a later part of our syllabus, okay. Because KVPY is happening in November, so I have to hurry up with respect to this particular topic, fine. So, those who are attempting KVPY, only for those, fine. Please attend this class 4.30pm to 7.30pm tomorrow, okay. So, that's it for today. I hope you have learned many things today. Go back and straight away, jump on to the problem solving and finish off the homework as soon as possible. And I would love to hear at least some of you finishing the homework in next two days itself, okay. Thank you very much.