Question

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

• A. ring
• B. solid sphere
• C. hollow sphere
• D. disc

Answer 1

The correct option is D disc

By the concept of energy conservation,
$\frac{1}{2}m{V}^2+\frac{1}{2}I\frac{V^2}{R^2}=mgh=\frac{3}{4}m{V}^2$
$\therefore \frac{1}{2}I\frac{V^2}{R^2}=\frac{3}{4}m{V}^2-\frac{1}{2}m{V}^2=\frac{1}{4}m{V}^2$
$\Rightarrow I=\frac{1}{2}m{R}^2$