Derive an expression for the gravitational potential energy of an object of mass 'm' at a height 'h' above the earth's surface.

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

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