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Two simple pendulums of lengths L and 4L are set into simple harmonic motion. It is observed that the maximum linear velocities of their bobs are equal. The ratio of their maximum angular displacements (angular amplitudes) ₁ : ₂ will be :

Options

  1. A1:2
  2. B4:1
  3. C2:1
  4. D1:4

Correct answer

C. 2:1

Step-by-step solution

The maximum linear velocity of a simple pendulum is given by v_ max = A , where A is the linear amplitude and is the angular frequency. For a simple pendulum of length L and maximum angular displacement ₀ , the linear amplitude is A = L ₀ . The angular frequency is = g L . Therefore, v_ max = (L ₀) g L = ₀ gL . Given that the maximum linear velocities are equal for both pendulums: ₁ gL₁ = ₂ gL₂ Substituting L₁ = L and L₂ = 4L : ₁ gL = ₂ g(4L) ₁ L = 2 ₂ L ₁ ₂ = 2 1 Thus, the ratio of their maximum angular displaceme

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