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AP EAMCET20227 Jul 2022Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Two wooden blocks of mass M₁ and M₂ rest on a frictionless table. A bullet of mass m is fired at M₁ with speed v which embedded in it and the two together finally collide with M₂ . Find the velocity of M₂ after collision. (Ignore any energy loss and treat the problem to be one dimensional)

Options

  1. A2 m v M₁+M₂+m
  2. Bm v M₁+M₂+m
  3. C(M₁+M₂+m ) v M₁+M₂+m
  4. DM₁+M₂ M₁+M₂+m v

Correct answer

A. 2 m v M₁+M₂+m

Step-by-step solution

( ) For an elastic collision of 2 masses m₁ and m₂ with initial velocities u₁ and u₂ , final velocities of masses after collision are v₁= ( m₁-m₂ m₁+m₂ ) u₁+ 2 m₂ u₂ (m₁+m₂ ) and v₂= ( m₂-m₁ m₁+m₂ ) u₂+ 2 m₁ u₂ m₁+m₂ These are obtained as standard results by applying conservation of energy and momentum equations. Now, in given case at first bullet is embedded in mass M₁ . Let speed of bullet + Block system be v₁ after collision. Then by conservation of momentum we have. aligned & m v= (m+M₁ ) v₁ & or v₁= ( m v m+M₁

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