Physics - Circular Motion Question with Solution | TestHub
Two friends A and B (each weighing 40 kg) are sitting in a frictionless well having vertical circular smooth wall. They subtend angle 90° at the centre of the well. A rolls a ball of mass 40 kg in the clockwise direction on the platform base towards B along the wall of the well, which B catches. Then similarly B rolls the ball towards A anticlockwise and A catches it. The ball has a fixed speed of 5 m/s. (Neglect catching and throwing time).
Find the angular displacement of A till he meets B
Options:
Answer:
Solution:
Phase 1: A throws the ball at 5 m/s relative to himself. Equal masses (40 kg each) give the ball 2.5 m/s clockwise and A 2.5 m/s anticlockwise along the wall. The ball sweeps 90 degrees from A to B; in the same time A also sweeps 90 degrees anticlockwise, so A ends up diametrically opposite B. B catches the ball: ball + B (80 kg) move at 1.25 m/s clockwise. Phase 2: B rolls the ball back at 5 m/s relative to himself. Momentum conservation on (B + ball): 80 x 1.25 = 40 v_b - 40 w with v_b + w = 5, giving B 3.75 m/s clockwise and the ball 1.25 m/s anticlockwise. A keeps coasting at 2.5 m/s anticlockwise, gains on the ball at (2.5 - 1.25)/R = 1.25/R rad/s across the 180 degree gap, and catches it after exactly one full revolution; in the same time B, drifting at 3.75/R, covers 540 degrees and arrives at the very same point - they meet there. A's net angular displacement from his starting point is therefore 90 degrees. Answer: (C) 90 degrees.
