Question

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

Answer 1

From the Law conservation of momentum
`mv = m_(1)(v_(1) - (v_(1)/(3)))` or `v = (m_(1))/(m) xx (2v_(1))/(3)`
To decribe a vertical circle `v = sqrt(55 gl)`
hence `sqrt(5gl) = (m_(1))/(m) xx (2v_(1))/(3) rArr v_(1) = (m)/(m_(1)) xx (3 sqrt(5gl))/(2)`.