Question

For a body rolling along a level surface. Without slipping the translation and rotational kinetic energy are in the ratio $2:1$. The body is

• A. Hollow sphere
• B. Solid cylinder
• C. Ring
• D. Solid sphere

Answer 1

The correct option is B Solid cylinder

Let Moment of Inertia $I$, mass $m$, Radius $R$ and speed $v$

Body is rolling without slipping, $\Rightarrow v=R\omega$

Translational Kinetic energy(TKE) $=\frac{1}{2}m{v}^2$

Rotational Kinetic Energy (RKE) $=\frac{1}{2}I{\omega }^2=\frac{I{v}^2}{2R^2}$

$\Rightarrow \frac{TKE}{RKE}=2=\frac{\frac{1}{2}m{v}^2}{\frac{I{v}^2}{2R^2}}$

$\Rightarrow I=\frac{1}{2}m{R}^2$

Hence, Body is solid cylinder.