00:01
Hello, in the question we have given that a solid 8 kg ball rolls up.
00:06
So, mass is given which is of 8 kgs and it rolls up an incline which has an inclination of 30 degrees from the horizontal.
00:16
So, at the bottom of the incline, the velocity of center of mass is found to be 15 m per second.
00:22
So, the velocity is given to be 15 m per second and so it is rolling at that point.
00:30
So, what is the kinetic energy? what is the initial kinetic energy of the ball? so, we have to find out the initial kinetic energy.
00:39
Now see it is rolling also and it is translating also.
00:42
So, see what will happen.
00:45
So, this is the incline let us say and here this angle out here is 30 degree.
00:51
So, over here from the bottom it starts rolling.
00:54
So, it is rolling also and it is translating also.
00:57
So, we will have both the kinetic energy.
00:59
So, the part a will be the kinetic energy will be the sum of like total kinetic energy will be rotational kinetic energy plus the translational kinetic energy.
01:33
So, this will be the total kinetic energy.
01:35
So, now then kinetic energy will be rotational kinetic is half i omega square plus the translational energy is simply half mb squared.
01:45
Now, see over here i it is given that it is a solid solid ball.
01:52
So, we can consider it as a sphere.
01:54
So, for sphere the moment of inertia is 2 by 5 m r square.
01:59
Now, this omega now see we do not know what is r.
02:03
So, this omega we will write in terms of v square by r square because i know that v is equals to r omega.
02:11
So, from here omega will be equal to v by r.
02:15
So, this is square.
02:16
So, i have just squared over here.
02:17
So, this r square r square will go away and your half mv square is there as it is.
02:23
Now, following this what we will get is so it will be this two will get cancelled.
02:28
So, we will get 1 by 5 mv square plus half mv square.
02:35
So, if we calculate this, so, this will be 7 by 10 mv square.
02:40
So, this is the kinetic energy.
02:42
Now, just plug the values and we will get what is the kinetic energy over there.
02:46
So, kinetic energy will be 7 by 10 into mass is 8 into velocity is 15 times 15...