What is the minimum velocity with which a body of mass m must enter at the bottom of a vertical loop of radius R so that it can complete the loop?

Let the body enter a vertical loop of radius ‘R’ with a velocity ‘u’ and the body has a velocity ‘v’ at the topmost point in the vertical loop.
At the topmost point, normal force is zero. Acceleration due to gravity will be the centripetal acceleration.

$\Rightarrow \frac{{\mathrm{v}}^2}{\mathrm{R}}=\mathrm{g}\Rightarrow {\mathrm{v}}^2=\mathrm{gR}$.....(1)

From the bottom-most point to top most  point, the body will raise by ‘2R’

$\Rightarrow \frac{1}{2}m{u}^2-\frac{1}{2}m{v}^2=mg\left(2R\right)$

using (1)  

we get   $\frac{1}{2}m{u}^2-\frac{1}{2}m\left(gR\right)=mg2R$

$\Rightarrow \mathrm{u}=\sqrt{5\mathrm{gR}}$