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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

Determine the ratio of the linear momenta for two particles having masses of 1.0 kg and 4.0 kg , given that they possess equal kinetic energies.

Options

  1. A2 : 1
  2. B1 : 16
  3. C1 : 2
  4. D1 : 4

Correct answer

C. 1 : 2

Step-by-step solution

The kinetic energy K and linear momentum p of a particle of mass m are related by the expression: K = p^2 2m Rearranging for momentum p , we get: p = 2mK Given that the two particles have equal kinetic energies, K₁ = K₂ = K . The ratio of their linear momenta is: p₁ p₂ = 2m₁K 2m₂K = m₁ m₂ Substituting the given masses m₁ = 1.0 kg and m₂ = 4.0 kg : p₁ p₂ = 1.0 4.0 = 1 4 = 1 2 The ratio of their linear momenta is 1 : 2 .

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