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