A small ball of mass m is placed in a circular tube of negligible width, mass M and radius R which is kept on a horizontal plane in gravity free space. Friction is absent between tube and ball. Ball is given a velocity $v_{0}$ as shown. Then,

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In the COM frame both the ball and the tube centre move in circles about the COM - (A) true, (B) false. Normal: relative centripetal R v 0 2 ​ ​ = N ( m 1 ​ + M 1 ​ ) ⇒ N = ( m + M ) R m M v 0 2 ​ ​ . Ball's ground acceleration = m N ​ , so curvature radius = N / m v 0 2 ​ ​ = M ( m + M ) R ​ , not m + M MR ​ - (C) false. M = 2 m : N = 3 m R 2 m 2 v 0 2 ​ ​ = 3 R 2 m v 0 2 ​ ​ − ( D ) true. Answer: (A), (D)

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