Q 11-05-154JEE MainJEE Main 2021 (27 Aug, Shift 2)Medium
A bullet of $10$ g, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100$ m s$^{-1}$. The length of the pendulum is $0.5$ m and mass of the bob is $1$ kg. The minimum value of $v$ in m s$^{-1}$, so that the pendulum describes a circle. (Assume the string to be inextensible and $g = 10$ m s$^{-2}$)
Numerical value type. Enter your answer.
Answer: 400
To complete a vertical circle, the bob needs a speed at the bottom of $\sqrt{5gl} = \sqrt{5\times10\times0.5} = 5$ m s$^{-1}$.
Momentum conservation (bullet recoils backward):
$$0.01v = 0.01(-100) + 1\times5 \Rightarrow 0.01v = 4 \Rightarrow v = 400\ \text{m s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics