Question

A simple pendulum clock that keeps correct time on the earth is taken to the moon. It will run:

• A. At correct rate
• B. $6$ times faster
• C. $\sqrt{6}$ times faster
• D. $\sqrt{6}$ times slower

Answer 1

The correct option is D $\sqrt{6}$ times slower

The time period of simple pendulum on earth is
$T_E=2\pi \sqrt{L/g_E}$
Where $L$ is the length of simple pendulum. Now if take it to the moon, then
$T_m=2\pi \sqrt{L/g_m}$ but $g_m=\frac{g_E}{6}$
So $T_m=2\pi \sqrt{\frac{L\times 6}{g_E}}=\sqrt{6}{T}_E$