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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.


Solution

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)

 

Physics

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