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 $v_1$. The bullet emerges out of the bob with a speed of $v_1/3$ and the bob just complete motion along a vertical circle, then $v_1$ is :

• A. $\frac{3m}{2m_1}\sqrt{5gl}$
• B. $\frac{m_1}{m}\sqrt{5gl}$
• C. $\frac{2m}{3m_1}\sqrt{5gl}$
• D. $\frac{m_1}{m}\sqrt{gl}$

Answer 1

The correct option is A $\frac{3m}{2m_1}\sqrt{5gl}$

$speedofthebobjustafterthebulletisemergedfromitis\sqrt{5gl}asitjustcompletestheverticalcircularmotion.NowConservationoflinearmomentum{m}_1{v}_1=\frac{m_1{v}_1}{3}+m\sqrt{5gl}\Rightarrow v_1=\frac{3m}{2m_1}\sqrt{5gl}$