posted by Ellie on .
At what rate will a pendulum clock run on the Moon, where the
acceleration due to gravity is 1.63 m/s2 , if it keeps time accurately on
Earth? That is, find the time (in hours) it takes the clock’s hour hand to
make one revolution on the Moon.
provide solutions and explanations please, thank you in advance :D
The acceleration of gravity (g) is 9.81 m/s^2 on Earth and 1.63 m/s^2 on the moon. It is therefore higher on Earth by a factor of 6.02.
The period of a pendulum is
P = 2 pi sqrt(L/g)
Since you are using the same clock in both places, L stays the same and the period will be longer by a factor sqrt6.01 = 2.45 on the moon.
On Earth, a clock's hour hand takes 12 hours to make a complete revolution. Multiply that by 2.45 for the equivalent time on the moon.
In get 29.4 hours