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JEE Advanced2011PhysicsCenter of Mass, Momentum and CollisionActual

A thin ring of mass 2 ~kg and radius 0.5 ~m is rolling without slipping on a horizontal plane with velocity 1 m / s . A small ball of mass 0.1 ~kg , moving with velocity 20 ~m / s in the opposite directions, hits the ring at a height of 0.75 ~m and goes vertically up with velocity 10 m / s . Immediately after the collision

Options

  1. Athe ring has pure rotation about its stationary CM
  2. Bthe ring comes to a complete stop
  3. Cfriction between the ring and the ground is to the left
  4. Dthere is no friction between the ring and the ground

Correct answer

A. the ring has pure rotation about its stationary CM

Step-by-step solution

The data is incomplete. Let us assume that friction from ground on ring is not impulsive during impact. From linear momentum conservation in horizontal direction, we have aligned & (-2 1)+(0.1 20) & =(0.1 0)+(2 v) -ve +v e aligned Here, v is the velocity of CM of ring after impact. Solving the above equation, we have v=0 Thus, CM becomes stationary. Correct answer is (a). Linear impulse during impact (i) In horizontal direction J₁= P=0.1 20=2 Ns (ii) In vertical direction J₂= P=0.1 10=1 Ns Writing the equation (abo

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