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

Correct Answer: 10

\(v_{bob}= \sqrt {5gI}\)
\(v_{bob}= \sqrt {5 \times 10 \times 2}\)
\(v_{bob}= 10\ m/s\)
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 \(10\ m/s\).