posted by gino intili on .
It is the year 2305 and the tallest structure in the world has an insane height of 3.19×106 m above the surface of the Earth. A pendulum clock that keeps perfect time on the surface of the Earth is placed at the top of the tower. How long does the clock take to register one elapsed hour? The radius of the Earth is 6.38×106 m and its mass is 5.97×1024 kg.
You don't need to know the mass of the Earth in this case.
The value of g at the top of the tower, g', will be less than the earth-surface value, which must be multiplied by
[6.38/(3.19 + 6.38)]^2 = (2/3)^2
g' = (4/9)*g
The pendulum period is proportional to 1/sqrtg , a factor that becomes 3/2 at the top of the tower.
It will therefore take the clock 90 minutes to indicate a one hour change.