Question

A pendulum of length $2m$ consists of a wooden bob of mass $50g.$ A bullet of mass $75g$ is fired towards the stationary bob with a speed $v.$ The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the verical circle. The value of $v$ is________ $m{s}^{-1}$. $\left({\text{if g = 10 m/s}}^2\right).$

Answer 1

As bob is just completing the circle so,
$v_{\text{bob}}=\sqrt{5gl}=\sqrt{5\times 10\times 2}=10m/s$

Conserving momentum:
$75\times v=75\times \frac{v}{3}+50\times 10$
$\Rightarrow 50v=50\times 10$
$\Rightarrow v=10m/s$