A body of mass m kg starts falling from a distance 2R above the earth's surface. What is its kinetic energy when it has fallen to a distance 'R' above the earth's surface ? (where R is the radius of Earth)

Explanation

By conservation of mechanical energy,
`- (GMm)/(3R)+0=- (GMm)/(2R)+K.E. implies K.E. =(GMm)/R[1/2-1/3]=1/6 (GMm)/R=1/6 ((gR^(2))m)/R=1/6 mgR`.