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COMEDK2025PhysicsCenter of Mass, Momentum and CollisionActual

Momentum of a body is increased to three times its original value. By what percentage will its kinetic energy change?

Options

  1. A800 %
  2. B200 %
  3. C900 %
  4. D300 %

Correct answer

A. 800 %

Step-by-step solution

The kinetic energy K of a body is related to its momentum p by the formula K = p^2 2m , where m is the mass of the body. Let the initial momentum be p₁ = p and the initial kinetic energy be K₁ = p^2 2m . The momentum is increased to three times its original value, so the new momentum is p₂ = 3p . The new kinetic energy K₂ is given by K₂ = p₂^2 2m = (3p)^2 2m = 9p^2 2m = 9K₁ . The change in kinetic energy is K = K₂ - K₁ = 9K₁ - K₁ = 8K₁ . The percentage change in kinetic energy is K K₁ 100 % = 8K₁ K₁ 100 % = 800 % .

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