A body of mass m kg. starts falling from a point 2R above the earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the earth’s surface [R-Radius of earth, M-Mass of earth, G-Gravitational constant] :

(1/6) [(GMm)/R]

When body starts falling toward earth’s surface its potential energy decreases so kinetic energy increases. Increase in kinetic energy = Decrease in potential energy Final kinetic energy – Initial kinetic energy = Initial potential energy – Final potential energy Final kinetic energy – 0

 = \([\frac{-GMm}{r_1}] - [\frac{-GMm}{r_2}]\)

Thus, final kinetic energy : 

 = \([\frac{-GMm}{R + h_1}] - [\frac{-GMm}{R+h_2}]\)

 = \([\frac{-GMm}{R + 2R}] - [\frac{-GMm}{R+R}]\)

 = \([\frac{-GMm}{3R}]+[\frac{GMm}{2R}]\)

 = \(\frac{1}{6} \frac{GMm}{R}\)