A monkey jumps from ball A onto ball B which are suspended from inextensible light string each of length L. The mass of each ball & monkey is same. What should be the minimum relative velocity of jump w.r.t. ball, if both the balls manage to complete the circle?

Engineering

Physics

Momentum and Energy Conservation for System of Particles

Question

$\sqrt{5 gL}$

$\sqrt{20 gL}$

$4 \sqrt{5 gL}$

none

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

For both balls to complete a vertical circle, each must have a minimum speed of $\sqrt{5 g L}$ at the bottom. The monkey jumps from ball A to B. Using conservation of momentum for the jump, the relative velocity $v_{r e l}$ is found by ensuring both balls have the required speed. The calculation yields $v_{r e l} = \sqrt{20 g L}$ .

Final Answer: $\sqrt{20 g L}$