Question

A body of mass $M$ and radius $R$ is rolling on a horizontal plane with speed $v$. It then rolls up an inclined plane upto a height $h=\frac{v^2}{g}$. What is the nature of the body?

• A. Ring
• B. Solid sphere
• C. Spherical shell
• D. Cylinder

Answer 1

The correct option is A Ring

Let moment of inertia of body =$I$

Then initial kinetic energy = $\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2$

Final potential energy = $mgh$

$=mg\times \frac{v^2}{g}=m{v}^2$

$\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2=m{v}^2$

$\frac{1}{2}I{\omega }^2=\frac{1}{2}m{v}^2$

$I=\frac{m{v}^2}{{\omega }^2}=m{r}^2$

$\therefore$ Body is a $ring$