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Q.

A small ball (uniform solid sphere) of mass m is released from the top of a smooth wedge of the same mass m . The wedge is free to move on a smooth horizontal surface. The ball is sliding on the wedge. The  height of the wedge is as mentioned in the figure. Which of the following statement about the above system is/are true.

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a

The speed of the wedge when the ball is just going to leave the wedge at point 'P' of the wedge is = gh .

b

The total kinetic energy of the ball just before it falls on the ground is = (3118)mgh

c

The horizontal separation between the ball and the edge 'PQ' of wedge just before the ball falls on the ground is =2103h .

d

Horizontal component of the velocity of centre of the ball and the velocity of the wedge will be equal in magnitude at every instant.

answer is A, D.

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Detailed Solution

mvw-mvb=0 vw=vb mgh=12mv2+12mv2 1v=gh 212mv12+v2=mgh + mgh =2mgh 3 vrel=2gh 12gt2=h   t=2hg  Srel=vrelt=2gh×2hg=22h 4 Momentum of the system in horizontal direction is conserved.

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