Time period on the moon

A simple pendulum having time period 2 second on Earth is taken on the Moon. What will be its time period (in seconds) on Moon if it is given that the mass of the Earth is 81 times the mass of the Moon and the radius of the Earth is 4 times the radius of the Moon.

Details and assumptions:

  • The acceleration due to gravity at the surface of a planet is g = G M R 2 g = \dfrac{GM}{R^2} , where M is the mass of the planet and R is its radius.

  • The time period of a simple pendulum is T = 2 π L g T=2\pi \sqrt{\dfrac{L}{g}} , where L is the length of the simple pendulum.


The answer is 4.5.

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