A pendulum comsists 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` and it emerges from the bob with speed `v_1/3`. The bob just completes motion along a vertical circle. Then `v_1` is

Options

A. (a) `m/m_1sqrt(5gl)`
B. (b) `(3m)/(2m_1)sqrt(5gl)`
C. (c) `2/3(m/m_1)sqrt(5gl)`
D. (d) `(m_1/m)sqrt(gl)`

Answer

B

Explanation

Let velocity of m just after collision is v. Then, from conservation of momentum we have,
`m_1v_1=mv+m_1v_1/3implies:. v=2/3(m_1v_1)/(m)`
Now, for just completing the circle,
`v=sqrt(5gl)`
`:. 2/3(m_1v_1)/(m)=sqrt(5gl)`
`:. v_1=(3m)/(2m_1)sqrt(5gl)`