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

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Answer 1 · 2017-05-30T14:32:40

The period is #=14.7s#

The equation of the pendulum is

#T=2pisqrt(l/g)#

On earth, we have

#T_e=2pisqrt(l/g_e)#

#T_e=6s#

On the moon, we have

#T_m=2pisqrt(l/g_m)#

But,

#g_m=1/6g_e#

So,

#T_m=2pisqrt(l/(1/6g_e))#

#=2pisqrt((6l)/g_e)#

#=2pisqrt(l/g_e)*sqrt6#

So,

#T_m=sqrt6*T_e=6sqrt6=14.7s#