Question

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

• 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

KE is equal $I_1{\omega }_1^2=I_2{\omega }_2^2$

$\frac{{\omega }_1}{{\omega }_2}=\sqrt{\frac{I_1}{I_2}}$

inertia of hoop will be larger $I_2={mr}^2$

and

inertia of cylinder $I_1=\frac{1}{2}{mr}^2$

$since{I}_2>>I_1$

Hence, the cylinder has greater translational speed than the loop.