Question
Derive an expression for the potential energy stored in mass m in gravitational field of earth when placed at a height h above ground. Take surface of the earth as reference point for potential energy.
Solution
Consider,
A body of mass 'm' placed at the surface of the earth and moved from surface of the earth O to a point A at a height h from O.
Let at any instant, the body be at a height x from ground.
The small amount of work done by gravitational force in displacing the body by dx against gravity is,
Total amount of work done by gravitational force in displacing the body from ground to height h is,
Therefore the potential energy stored in the body is mgh.
A body of mass 'm' placed at the surface of the earth and moved from surface of the earth O to a point A at a height h from O.
Let at any instant, the body be at a height x from ground.
The small amount of work done by gravitational force in displacing the body by dx against gravity is,
Total amount of work done by gravitational force in displacing the body from ground to height h is,
Therefore the potential energy stored in the body is mgh.
