Question

A body is rolling down an inclined plane . its transational and rotational energies are equal . the body is

• A. solid sphere
• B. hollow sphere
• C. solid cylinder
• D. hollow cylinder

Answer 1

The correct option is D hollow cylinder

$\begin{array}{c}\text{Translational kinetic eneogy}=\frac{1}{2}m{v}^2\\ \text{and rotational kinetic energy}=\frac{1}{2}I{\omega }^2(\text{Here}V=\omega \text{r})\\ \text{Given, Translational}{k}_{.}E=\text{Rotationol}{k}_{.}E\end{array}$

$\begin{array}{cc}\Rightarrow \frac{1}{2}m{v}^2=\frac{1}{2}I{\omega }^2\Rightarrow & m\times {\omega }^2{R}^2=I{\omega }^2\\ & \therefore I=m{R}^2\\ \text{Thus, the body may be a hollow cylinder. (D).}& \end{array}$