Question
A simple pendulum clock keeps correct time at the sea level and loses 0.9 min per day at the top of a mountain. What is the height of the mountain?
Solution
The time period of simple pendulum clock at the surface of the earth is,
Let g' be the acceleration due to gravity at the top of mountain.
Then, time period of simple pendulum clock at the top of mountain is,
The acceleration due to gravity at the surface of the earth is,
where,
M is mass, and
R is the radius of the earth.
Let h be the height of the mountain.
Acceleration due to gravity at the top of the mountain is given by,
The loss of time of oscillation of simple pendulum clock in one second is, 
Thus loss of time of oscillation of simple pedulum clock in one day is,
Height of the mountain is 54 km.
