Question

a pendulum on earth has a period of 6.0 s. What is the period of this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that of Earth?

Answer 1

Period \(T\) for a pendulum with a small displacement angle is given by the following equation for string length \(\ell\) and gravitational acceleration \(g\).\[T=2\pi\sqrt{\frac{\ell}{g}}\]The ratio between the period of a pendulum on the earth \(T_e\) and the period of the same pendulum on the moon \(T_m\) is given as follows (for the moon, we substitute \(g\rightarrow g/6\)).\[\frac{T_m}{T_e}=\frac{2\pi\sqrt{\frac{\ell}{g/6}}}{2\pi\sqrt{\frac{\ell}{g}}}=\sqrt{6}\]Thus, \(\boxed{T_m=T_e\sqrt{6}}\), which I believe should be enough for you to solve the problem.

Answer 2

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Answer 3

No problem!