A simple pendulum having bob of mass m and length of string l has time period of T. If the mass of the bob is doubled and the length of the string is halved, then the time period of this pendulum will be

  1. A. T
  2. B. T/\sqrt{2} ✓
  3. C. 2T
  4. D. \sqrt{2}T

Correct Answer: B. T/\sqrt{2}

Explanation

The time period of a simple pendulum T = 2\pi\sqrt{\frac{l}{g}} is independent of the mass. If the length is halved (l' = \frac{l}{2}), the new time period T' = 2\pi\sqrt{\frac{l/2}{g}} = \frac{T}{\sqrt{2}}.

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