A pendulum consists of a wooden bob of mass `m` and length `l`. A bullet of mass `m_(1)` is fired towards the pendulum with a speed `v_(1)`. The bullet emerges out of the bob with a speed of `(v_(1))//3` and the bob just completes motion along a vertical circle, then `v_(1)` is

Options

A. `(3m)/(2m_(1))sqrt(5gl)`
B. `m_(1)/msqrt(5gl)`
C. `(2m)/(3m_(1))sqrt(5gl)`
D. `(m_(1))/msqrt(gl)`

Answer

B

Explanation

From conservation of mometum
`mv_(2)=m_(1)v_(1)//3=m_(1)v_(1)impliesv_(2)=(2m_(1)v_(1))/(3m)`

Now `v_(2)=sqrt(5gl)`
`(2m_(1)v_(1))/(3m)=sqrt(5gl)impliesv_(1)=(3m)/(2m_(1))sqrt(5gl)`