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NEETPhysicsCenter of Mass, Momentum and Collision

A particle of mass m moving with velocity v collides completely inelastically with a stationary particle of mass 3m . The percentage loss in the kinetic energy of the system due to the collision is:

Options

  1. A75 %
  2. B25 %
  3. C33 %
  4. D50 %

Correct answer

A. 75 %

Step-by-step solution

Using the principle of conservation of linear momentum: Initial momentum = Final momentum m v + (3m)(0) = (m + 3m) v_f m v = 4m v_f v_f = v 4 Initial kinetic energy of the system: K_i = 1 2 m v^2 Final kinetic energy of the combined system: K_f = 1 2 (4m) v_f^2 = 1 2 (4m) ( v 4 )^2 = 1 2 m v^2 ( 1 4 ) = K_i 4 Loss in kinetic energy: K = K_i - K_f = K_i - K_i 4 = 3K_i 4 Percentage loss in kinetic energy: K K_i 100 = 3 4 100 = 75 % Answer: 75 %

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