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NEETPhysicsCenter of Mass, Momentum and Collision

Statement-I: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-II: Principle of conservation of momentum holds true for all kinds of collisions.

Options

  1. ABoth Statement-I and Statement-II are correct.
  2. BBoth Statement-I and Statement-II are incorrect.
  3. CStatement-I is correct and Statement-II is incorrect.
  4. DStatement-I is incorrect and Statement-II is correct.

Correct answer

A. Both Statement-I and Statement-II are correct.

Step-by-step solution

Let masses (m₁, m₂ ) have initial velocities (u₁, u₂ ) in the same direction and they stick after collision (perfectly, inelastic). Common velocity (v= m₁ u₁+m₂ u₂ m₁+m₂ ) Initial KE: (K_i= 1 2 m₁ u₁^2+ 1 2 m₂ u₂^2, ) Final KE: (K_f= 1 2 (m₁+m₂ ) v^2 ) Loss of kinetic energy ( K=K_i-K_f= 1 2 m₁ m₂ m₁+m₂ (u₁-u₂ )^2 0 ) This loss is not the whole initial energy except when (u₁=u₂ ) (then ( K=0 )). So Statement-1 is true: they do not lose all their energy in general. Statement-II is also true: momentum is conserved in

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