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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)√5glLet the velocity of the bob after the collision be v.As the bob just completes the vertical circular motion ⟹v=√5glApply conservation of momentum just before and after the collision :m1v1+0=mv+m1v1m1v1=m×√5gl+m1×v13⟹v1=3m2m1√5gl

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