Question

A pendulum of length $2\ m$ consists of a wooden bob of mass $50\ g$. A bullet of mass $75\ g$ is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed $\frac v3$ and the bob just completes the vertical circle. The value of v is _______ $ms^{–1}$. (if $g=10\ m/s^2$).

Answer 1

$v_{bob}= \sqrt {5gI}$
$v_{bob}= \sqrt {5 \times 10 \times 2}$
$v_{bob}= 10\ m/s$
By the law of Conservation of Momentum,
$⇒ 75×v=75×\frac v3+50×10$
$⇒ 50v = 50 × 10$
$⇒ v = 10\ m/s$

So, the answer is $10\ m/s$.