A body initially at rest and sliding along a frictionless track from a height $h$ just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to:

1. To just complete a vertical circle of radius $R$, the minimum velocity at the lowest point must be $v=\sqrt{5gR}$.2. Using conservation of energy: Potential Energy at height $h$ = Kinetic Energy at the bottom.
$$mgh=\frac{1}{2}m{v}^2$$
$$mgh=\frac{1}{2}m(5gR)⟹h=\frac{5}{2}R$$
3. Given Diameter $D=2R$, so $R=D/2$.
$$h=\frac{5}{2}\left(\frac{D}{2}\right)=\frac{5}{4}D$$