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

  1. At correct rate.

  2. 6 times faster.

  3. $\sqrt{6}$ times faster.

  4. $\sqrt{6}$ times slower.

Answer

  1. $\sqrt{6}$ times slower.

Explanation:

The acceleration due to gravity at moon is $\frac{\text{g}}{6}. $

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

Therefore, on moon, time period will be:

$\text{T}_{\text{moon}}=2\pi\sqrt{\frac{\text{l}}{\text{g}_{\text{moon}}}}=2\pi\sqrt{\frac{\text{l}}{\Big(\frac{\text{g}}{6}\Big)}}$

$=\sqrt{6}\Big(2\pi\sqrt{\frac{\text{l}}{\text{g}}}\Big)=\sqrt{6}\text{T}$

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