A small body of mass m falls to the earth from an infinite distance away. What will be its velocity on reaching the earth? (Radius of the earth = R, acceleration due to gravity on the surface of the earth is g):

a) gR

b)2gR

c) √gR

d) √2gR

Solution:

change in potential energy = change in kinetic energy

ΔPE = ΔKE

mgR = (1/2)mv2 – 0

2gR = v2

v = √2gR