Question

A body of mass m is taken to a height kR from the surface of the earth very slowly,R being the radius of the earth. Find the change in gravitational potential energy in this process.

Answer 1

Initially the body is on the surface of Earth ie., at a distance of R from center of Earth. Its final position is (k+1)R from center of Earth.

From gravitational energy principles we have that:
Initial potential energy = - G Me m / R
Final potential energy = - GMe m / [(k+1)R ]

Change in PE = GMe m/R * [1 - 1/(k+1) ]
= GMe m/R * k/(k+1)
We know that GMe/R² = g

So change in PE = mgR * k/(k+1)