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)