Since, the initial velocity of body is zero, its total energy is
$E=\frac{-G m M}{r}$ ...(i)
where, $m$ is the mass of body, $M$ is the mass of the Earth and $r$ 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
$E=\frac{1}{2} m v^{2}-\frac{G M m}{R}$ ...(ii)
Equating Eqs. (i) and (ii), we get
$v^{2}=2 G M\left(\frac{1}{R}-\frac{1}{r}\right)$
Also, $g=\frac{G M}{R^{2}}$. Therefore, $G M=g R^{2}$.
Using this in the above equation, we get
$V=R\left[2 g\left(\frac{1}{R}-\frac{1}{r}\right)\right]^{1 / 2}$
Now, $r=2 R$ (given). Therefore,
$V=R\left[2 g\left(\frac{1}{R}-\frac{1}{2 R}\right)\right]^{1 / 2}$
$\Rightarrow $ Velocity of a body which strike the Earth's surface, $v=\sqrt{g R}$