Question

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

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

Answer 1

The correct option is D Disc

Moment of inertia of the object can be written as $I=km{r}^2$

At the highest point, the body stops moving upward as well stops rotating. So total kinetic energy of the body at the highest point is zero i.e. $K.E_f=0$

Initial kinetic energy of the body $K.E_i=\frac{1}{2}m{v}^2(1+k)$

Applying work energy theorem :

$W_{mg}=K.E_f-K.E_i$

Or $-mgh=0-\frac{1}{2}m{v}^2(1+k)$

Or $mg\times \frac{3v^2}{4g}=\frac{1}{2}m{v}^2\times (1+k)$

$⟹k=\frac{1}{2}$

Thus the given body must be a disc.