An object of mass `m` is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?

Explanation

P.E. of the object at height R from the surface of earth
`[P.E.]_(R ) = -(GmM)/(R )`
P.E. of the object at height 2R from the surface of earth
`[P.E.]_(2R) = -(GmM)/(2R)`
`:.` Gain in P.E. `= (P.E.)_(2R) - [P.E.]_(R )`
`= -(GmM)/(2R) + (GmM)/(R )`
`= + (GmM)/(2R)`
`= (1)/(2) mg R " "[because GM = gR^(2)]`