Question

What is meant by the gravitational potential energy ? Derive an expression for it for a body placed at a height above the ground.

Answer 1

An object increases its energy when raised through a height. The energy present in such an object is the gravitational-potential energy. This gravitational-potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

Any object on the earth is pulled towards the center of the earth with a force equal to the weight of the object. An object of mass ‘m’ will be pulled towards the earth’s center by a force equal to ‘mg’

So, to lift the object without any acceleration a force equal to its weight must be applied in the opposite direction (away from the center of the earth).

We have, Force = mg, to lift the object. Suppose, h is the height attained by the object due to this force. The work done by this force is stored as gravitational potential energy of the object.

Therefore, potential energy = work done = mgh