Question

A 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

(d) $\sqrt{6}$ times slower

The acceleration due to gravity at moon is g/6.

Time period of pendulum is given by, $T=2\pi \sqrt{\frac{l}{g}}$

Therefore, on moon, time period will be:

T_moon = $2\pi \sqrt{\frac{l}{g_{moon}}}=2\pi \sqrt{\frac{l}{\left({\displaystyle \raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}\right)}}=\sqrt{6}\left(2\pi \sqrt{\frac{l}{g}}\right)=\sqrt{6}T$