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?
As the object of mass m is lifted upwards from surface of earth to a height equal to the radius of earth i.e. from R→2R P.E. of body on the surface of earth = R−GMm P.E. of the object at a equal to the radius of earth =(2R)−GMm Gain in P.E.=Ef−Ei gain in P.E.=2R−GMm−(R−GMm) =RGMm[−21+1] =2RGMmGM=gR2 Gain in P.E.=2RgR2m=21mgR
