Question

A small object of uniform density rolls up a curved surface with in a initial velocity $v.$ It reaches up to a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is-

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

Answer 1

The correct option is A Disc

From conservation of mechanical energy,

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

We know that, for pure rolling, $v=\omega R$

$\frac{I}{2}\frac{v^2}{R^2}+\frac{1}{2}m{v}^2=mg\times \frac{3v^2}{4g}$

On solving, we get,

$I=\frac{m{R}^2}{2}\left[\text{which is for disc}\right]$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.