Question

at what rate will a pendulum clock run on uranus, where the accleration due to gravity is 9.01 m/s, iif it keeps time accuratley on earth?

Answer 1

If in earth the pendulum does a cycle in 1 second, in Uranus it will take 1.043 seconds.

At what rate will a pendulum clock run on uranus?

Period of a pendulum: The period (time for one complete swing) of a pendulum depends on its length (l) and the acceleration due to gravity (g) at the location:

T = 2π * √(l / g)

where π = 3.14

The period for each planet are:

Earth: T_Earth = 2π * √(l / 9.81)

Uranus: T_Uranus = 2π * √(l / 9.01)

Dividing these equations, we get:

T_Uranus / T_Earth = √(9.81 / 9.01) = 1.043

This means the period on Uranus is about 4.3%.

So, if the pendulum does one complete path in one second, the same pendulum in uranos will do a complete path in:

1s*1.043 = 1.043 seconds.