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The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?

Options

  1. A3 : 1
  2. B2 : 5
  3. C2 : 1
  4. D3 : 2

Correct answer

C. 2 : 1

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g . The time period is independent of the mass of the bob. Given that the new length is l₂ = 4l₁ . The new time period is T₂ = 2 l₂ g = 2 4l₁ g = 2 2 l₁ g = 2T₁ . The ratio of the new and previous time period is T₂ T₁ = 2 1 . Answer: 2 : 1

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