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Two simple pendulums start oscillating together from their mean position in the same phase. They are found to be in the same phase again at the mean position after the shorter pendulum completes 5 oscillations and the longer pendulum completes 4 oscillations. The ratio of the length of the longer pendulum to the length of the shorter pendulum is

Options

  1. A5 : 4
  2. B16 : 25
  3. C25 : 16
  4. D4 : 5

Correct answer

C. 25 : 16

Step-by-step solution

Let the time periods of the shorter and longer pendulums be T_S and T_L respectively. According to the given condition, both pendulums are in phase again when the shorter pendulum completes 5 oscillations and the longer pendulum completes 4 oscillations in the same time interval. Therefore, 5T_S = 4T_L T_L T_S = 5 4 The time period of a simple pendulum is given by T = 2 l g , which means T l . l_L l_S = ( T_L T_S )^2 = ( 5 4 )^2 = 25 16 Thus, the ratio of the length of the longer pendulum to the length of the short

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