• # question_answer 23) A body of radius R and mass m is rolling horizontally without slipping with speed u. It then rolls up a hill to a maximum height $h=\frac{3{{u}^{2}}}{4g}.$The body might be A) solid sphere                 B) hollow sphereC)      disc                D)      ring

Total $K.E=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}m{{u}^{2}}+\frac{1}{2}I..\frac{{{u}^{2}}}{{{R}^{2}}}$ $\left[ \because \,\omega =\frac{u}{r} \right]$ According to the law of conservation of energy loss in $K.E.=$gain in P.E. or $\frac{1}{2}\left( m+\frac{1}{{{R}^{2}}} \right){{u}^{2}}=mgh=mg\left( \frac{3{{u}^{2}}}{4g} \right)$ Solving this we get$I=\frac{1}{2}M{{R}^{2}}$ the solid body is a disc. Hence, the correction option is (c).