Three bodies a ring, a solid cylinder and a solid sphere roll down an inclined plane without slipping. They start from rest. Which of the bodies reaches bottom of plane with minimum velocity?

Say, the radius of gyration of the body is $K$.
The mass is $m$.
The height is $h$.
The radius of the body is $R$.
According to the conservation of mechanical energy,$mgh=\frac{1}{2}m{v}^2\left(1+\frac{K^2}{R^2}\right)$ or $v^2=\left(\frac{2gh}{1+\frac{K^2}{R^2}}\right)$
Note: It is independent of the mass of the rolling body.
For a ring, $K^2=R^2$
So, the speed of the ring becomes,$v_{ring}=\sqrt{\frac{2gh}{1+1}}=\sqrt{gh}$
For a solid cylinder, $K^2=\frac{R^2}{2}$
$v_{cylinder}=\sqrt{\frac{2gh}{1+\frac{1}{2}}}=\sqrt{\frac{4gh}{3}}$
For a solid sphere, $K^2=\frac{2}{5}{R}^2$
$v_{sphere}=\sqrt{\frac{2gh}{1+\frac{2}{5}}}=\sqrt{\frac{10gh}{7}}$
Among the given three bodies, the solid sphere has the greatest and the ring has the least velocity at the bottom of the inclined plane.