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KCET2026PhysicsCenter of Mass, Momentum and Collision

Two bodies with kinetic energies in the ratio of 3:1 are moving with equal linear momentum. The ratio of their masses is

Options

  1. A1:4
  2. B1:3
  3. C1:2
  4. D1:1

Correct answer

B. 1:3

Step-by-step solution

The kinetic energy K of a body is related to its linear momentum p and mass m by the relation: K = p^2 2m Since the linear momenta of the two bodies are equal ( p₁ = p₂ = p ), the kinetic energy is inversely proportional to the mass: K 1 m Therefore, the ratio of their masses is: m₁ m₂ = K₂ K₁ Given that the ratio of their kinetic energies is K₁ K₂ = 3 1 , we get: m₁ m₂ = 1 3 The ratio of their masses is 1:3 . Answer: 1:3

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