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MHT CET202525 Apr 2025Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

An object of mass ' m ' moving with velocity ' u ' collides with another stationary object of mass ' M ' and stops just after the collision. The coefficient of restitution is

Options

  1. Am M + m
  2. BM-m M+m
  3. Cm M
  4. D1

Correct answer

C. m M

Step-by-step solution

Coefficient of restitution determination: Conservation of linear momentum applied to the collision yields m u + M 0 = m 0 + M v₂ , which simplifies to m u = M v₂ and thus v₂ = m u M . The coefficient of restitution is defined as e = v₂ - v₁ u₁ - u₂ . Substituting the known velocities v₁ = 0 , u₂ = 0 , and the expression for v₂ gives e = m u M - 0 u - 0 = m M . The result e = m M corresponds to option C.

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