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Question

Figure shows a block A of mass 8m having a smooth semi circular groove of radius a placed on a smooth horizontal surface. A block B of mass m is released from a position in groove, where its radius is horizontal. The speed of block A when block B reaches its bottom is

A
ga
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B
2ga7
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C
ga36
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D
zero
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Solution

The correct option is C ga36
Let
v2= speed of block A towards left,
v1= speed of block B w.r.t. A towards right,
v1v2=speed of block B towards right.

By conservation of momentum,
8mv2=m(v1v2)
9v2=v1


By conservation of energy
mga=12×8m×v22+12×m×(v1v2)2
ga=4v22+12(9v2v2)2
ga=36v22
v2=ga36
(c)

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