Pendulumn on Moon Problem - Explained

 

 

 

 

 

 

 

 

 

 

A pendulum clock that keeps correct time on earth if taken to the moon it will slow down, Here it is explained why,

For small-ish oscillations, we know that period, T, of an oscillation is $T=2\pi \sqrt{\frac{l}{g}}$ where l is the length of the pendulum and g is prevailing gravity
as $g_{moon}\approx \frac{g_{earth}}{6}$
then $T_{moon}\approx 6\cdot T_{earth}$
So, if you like, a tick and a tock should take 6 times longer and the clock should run slow.