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. `m/m_(1)sqrt5gl`
B. `(3m)/(2m_(1))sqrt(5gl)`
C. `2/3(m/m_(1))sqrt(5gl)`
D. `(m_(1)/m)sqrt(gl)`

Answer

B

Explanation

From conservation of linear momentum,
`m_(1)v_91) = msqrt5gl) + m_(1)(v_(1)/3)` or `v_(1) = 3/2m/m_(1)sqrt(5gl)`