The change in the gravitational potential energy when a body of mass m is raised to a height n R above the surface of the earth is (here R is the radius of the earth)

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Gravitational potential energ at any point at a distance r from the centre of earth is U = − r GM m ​ At the surface of earth r = R , ∴ U s ​ = − R GM m ​ = − m g R ( ∵ g = R 2 GM ​ ) At the height h = n R from the surface of earth r = R + h = R + n R = R ( 1 + n ) ∴ U h ​ = − R ( 1 + n ) GM m ​ = − ( 1 + n ) m g R ​ Change in gravitational potential energy is Δ U ​ = U h ​ − U s ​ = − ( 1 + n ) m g R ​ − ( − m g R ) = − 1 + n m g R ​ + m g R ​ = m g R ( 1 − 1 + n 1 ​ ) = m g R ( 1 + n n ​ )

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