 Let's solve a couple of questions on conservation of energy. For the first one we have two blocks. Block A falls vertically from height H, block B is thrown downward with an initial speed of V from the same height H and the blocks are identical, which means they have the same mass. Which block hits the ground with the greatest speed? And you have to choose one answer out of these four options. As always, hit pause and try this one on your own first. I hope you have given this a shot. Now here we can look at this situation from the lens of conservation of energy. So when we do that we must go back to what was the principle of conservation of energy. If we just look at block A to begin with, so the total mechanical energy that the block A has at height H is equal to the total mechanical energy that the block A will have when it touches the ground. So when we write that this is k, k initial of A plus potential energy initial of A. This is equal to the final mechanical energy of A plus the final potential energy of A. And we can see that when block A reaches the ground there is there will be no potential energy, right? This will be zero. And this block A it is starting from height H but it is starting from rest. There is no velocity. So initial mechanical energy is also zero. So the block A's kinetic energy will just be equal to the initial potential energy of block A. And if you consider this mass as m, this will be mgh, that will be the kinetic energy, the final kinetic energy of block A. Now let's look at block B. Again block B we can consider the system as this block and the earth and within this system there will be just transformation of energy, the energy will be conserved. So the total mechanical energy, the total initial mechanical energy of block B will be equal to the total final mechanical energy for block B. And when we write that, when we write that, that will be k initial of B plus potential energy initial of B. This is equal to the final kinetic energy of B plus the final potential energy of B. And B is also touching the ground so that the final potential energy, this will be zero. Initially, it is moving with a speed. There is some kinetic energy that block B has. And it also has the same amount of potential energy as block A. So final kinetic energy for block B is not just equal to the potential energy for block B. It is also equal to the kinetic energy that the block B has initially. So this is a greater number, this is a greater number, this will be mgh and you are adding something to mgh. So the final kinetic energy will be more for block B. So this is block B because the final kinetic energy is more for block B. Its speed will also be more when it reaches the ground. Okay, let's move on to the next question now. Here we have a cart which is pushed into a short spring. We can see that over here. And then released from rest. Okay, it's starting from zero velocity. The cart follows the pathway shown in the diagram. So it goes like this, then falls down, then goes forward, then goes up. Passes through positions one to four. The spring only touches the cart at the first position. The cart has no height at position three. And the cart reaches the maximum height at the last position. The height of zero, y equals to zero is marked on the diagram. We can see that over here. There is no significant friction within the car or between the car and track. And we need to select the types of energy. There are three types. There is kinetic energy, there is gravitational potential energy and there is elastic potential energy, US, for the cart earth spring system, as the cart is at each of the four positions. All right, why don't we pause the video and try to select the types of energy at these four positions. So when we consider the cart earth spring system, we can think of it as a closed system. And there is no friction anyway. So all the energy transformations, they will happen within this system. They will be gravitational potential energy, spring elastic energy transforming into kinetic or kinetic gravitational transforming into spring. There will be all sorts of transformations. So here the spring, the elastic potential energy of the spring, that will be changed to the kinetic energy of the cart, which could then be changed to gravitational potential energy. So let's look at the first position. In the first position, we have the compressed spring. So there is some elastic potential energy. And this cart, it is also at a certain height. It is from y equals to zero level, it is at a certain height. So there is some gravitational potential energy as well at position one. At position two, the spring is not compressed. So there is no elastic potential energy. But that elastic potential energy is now changed to kinetic energy because now the cart is moving to the left with some velocity. There is some kinetic energy and there is still some gravitational potential energy because even at this point, the cart is at a certain height from y equals to zero. From y equals to zero. All right, now, let's see what happens then. Let's see at position three. So at position three, the cart is still moving to the left. But here there is no gravitational potential energy because it is at y equals to zero. So it's just the kinetic energy of the cart. And again, the spring is not compressed. So there is no elastic potential energy. At position four, v is zero. So there is no kinetic energy. There is no elastic potential energy. All that there is is only the gravitational potential energy. And this gravitational potential energy will really be different from these two gravitational potential energies because they were at this much height, this much height. And this gravitational potential energy is at a much, much greater height. We can call it h dash, much greater height. So we see that energy transformations happen within a closed system. There can be one type of energy which is then changed to another type of energy. But the total energy of the system remains constant. So the total energy of the system at position one is equal to the total energy of the system at position two, which is same as the total energy at position three and the total energy at position four.