Question

In which of the following cases of rolling body, translatory and rotational kinetic energies are equal

• A. Circular ring
• B. Circular plate
• C. Solid sphere
• D. Solid cylinder

Answer 1

The correct option is A Circular ring

${KE}_{rollingofRing}=\frac{1}{2}I{\omega }^2$
$V=\omega R$
$=\frac{1}{2}m{R}^2{\omega }^2$
$=\frac{1}{2}m{V}^2$ (on replacing the above initial equation)
${KE}_{Translational}=\frac{1}{2}m{V}^2$
Happens only in the case of circular ring because $K$$=$$R$ , $K$ is the radius of gyration.Hence both the energies are equal.