Question

A hoop and the solid cylinder have the same mass and radius. They both roll, without slipping, on a horizontal surface. If their kinetic energies are equal

• A. The hoop has a greater translational speed than the cylinder
• B. The cylinder has a greater translational speed than the hoop
• C. The hoop and the cylinder have the same translational speed
• D. The hoop has a greater rotational speed than the cylinder

Answer 1

The correct option is B The cylinder has a greater translational speed than the hoop

Moment of inertia of solid cylinder is
$I_s=\frac{1}{2}m{r}^2$

and for hoop moment of inertia is
$I_s=\frac{1}{2}m(r_o+r_i{)}^2$ (since it possesses inner radius also)

Hence, solid cylinder has moment of inertia smaller than the hoop. Hence, it has less resistance to rotational motion thus will accelerate faster than hoop and reaches to the bottom of inclined plane first.