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(2gl)`
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

Using conservation of linear momentum, `m_1v_1 = msqrt(5 gl) + m_(1) (v_1)/(3) implies V_1 = (3m)/(2m) sqrt(5gl)`.