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)))sqrt(5gl)`
B. `(3)/(2)((M)/(M_(1)))sqrt(5gl)`
C. `(3)/(2)((M_(1))/(M))sqrt(5gl)`
D. `((M_(1))/(M))sqrt(gl)`

Answer

B

Explanation

`M_(1)V_(1)=M_(t)(V_(1))/(3)+Msqrt(5fL)`
`V_(1)=(3Msqrt(5gL))/(2M_(1))`