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JIPMER2017PhysicsCenter of Mass, Momentum and Collision

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed V collides elastically with the stick as shown in fig below. If after the collision, the ball comes to rest, then what should be the mass of the ball?

Options

  1. Am=2 M
  2. Bm=M
  3. Cm=M / 2
  4. Dm=M / 4

Correct answer

D. m=M / 4

Step-by-step solution

Applying the law of conservation of momentum m V=M V...(i) By conservation of angular momentum m V(L / 2)= ( M L^2 12 ) ...(ii) As the collision is elastic, we have 1 2 m V^2= 1 2 M V^2+ 1 2 I w^2...(iii) Substituting the values, we get m=M / 4

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