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Question

A pendulum consists of a wooden bob of mass m and of length l. A bullet of mass m1 is fired towards the pendulum with a speed v1. The bullet emerges out of the bob with a speed v1/3 and the bob just completes motion along a vertical circle. Then v1 is :

A
(mm1)5gl
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B
32(mm1)5gl
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C
23(m1m)5gl
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D
(m1m)5gl
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Solution

The correct option is B 32(mm1)5gl
Let the velocity of the bob after the collision be v.
As the bob just completes the vertical circular motion v=5gl
Apply conservation of momentum just before and after the collision :
m1v1+0=mv+m1v1
m1v1=m×5gl+m1×v13
v1=3m2m15gl

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