since, the initial velocity of body is zero, its total energy is
E=....(i)
where,
m is the mass of body,
M is the mass of the Earth and
I its distance from the centre of the Earth. When the body reaches the Earth, let its, velocity be
v and its distance from the centre of the Earth equals the Earths radius
R. Therefore, the energy is
E=mv2−....(ii)
Equating Eqs. (i) and (ii), we get
v2=2GM(−) Also,
g=. Therefore,
GM=gR2.
Using this in the above equation, we get
v=R[2g(−)]1/2 Now,
r=2R (given). Therefore,
v=R[2g(−)]1/2 ⇒ Velocity of a body which strike the Earth's surface,
v=√gR