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NEETPhysicsCenter of Mass, Momentum and Collision

A moving object of mass 3 kg and velocity (4 i + 4 j ) m/s breaks into two pieces of masses 1 kg and 2 kg . If the 1 kg piece moves with a velocity of (4 i - 2 j ) m/s immediately after the explosion, the kinetic energy released during the explosion is

Options

  1. A75 J
  2. B27 J
  3. C48 J
  4. D12 J

Correct answer

B. 27 J

Step-by-step solution

By the principle of conservation of linear momentum: P _ initial = P _ final M v = m₁ v ₁ + m₂ v ₂ Substituting the given values: 3(4 i + 4 j ) = 1(4 i - 2 j ) + 2 v ₂ 12 i + 12 j = 4 i - 2 j + 2 v ₂ 2 v ₂ = (12 - 4) i + (12 + 2) j 2 v ₂ = 8 i + 14 j v ₂ = 4 i + 7 j m/s Now, calculate the initial kinetic energy ( K_i ): K_i = 1 2 M | v |^2 = 1 2 3 (4^2 + 4^2) = 1 2 3 32 = 48 J Calculate the final kinetic energy ( K_f ): K_f = 1 2 m₁ | v ₁|^2 + 1 2 m₂ | v ₂|^2 K_f = 1 2 1 (4^2 + (-2)^2) + 1 2 2 (4^2 + 7^2) K_f = 1 2

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