Question

A body of radius $R$ and mass m is rolling horizontally without slipping with speed $v$ . It then rolls up a hill to a maximum height $h=\frac{3v^2}{4g}$ . The body might be a

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

Answer 1

Answer: (C)

Let $I$ bt the moment of inertia of the body. Then total $KE=\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2$
or $\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}\mathrm{I}\frac{v^2}{R^2}\left(\omega =\frac{v}{R}\right)$
According to energy conservation loss in $KE=gain$ in $PE$ .
or $\frac{1}{2}\left(m+\frac{I}{R^2}\right)v^2=mgh=mg\left(\frac{3v^2}{4g}\right)$
Solving this, we get $I=\frac{1}{2}m{R}^2$
i.e., the solid body is a disc