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Q.

A pendulum consists of a wooden bob of mass m and 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 v1is

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a

mm15gℓ

b

32mm15gℓ

c

23m1m5gℓ

d

m1mgℓ

answer is B.

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Detailed Solution

Using conservation of momentum,m1v1+0=m1v13+mv⇒m1v1−m1v13=mv​(v=5gl to complete motion along vertical circle) ​⇒2 m1v13=mv⇒v=23m1v1 m or v1=32mm15gl
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