A body of mass m slides down an incline and reaches the bottom with a velocity $v$. If the same mass

Question

A body of mass m slides down an incline and reaches the bottom with a velocity $v$. If the same mass were in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been\

Professor PC Thomas Classes · Answer

Let $h$ be the height of plane. Source of KE at the bottom = PE at the top.\ Case I : Body sliding\ $\frac{1}{2} m v^{2}=m g h$\ Case II : Ring rolling\ Total KE $=\mathrm{m}\left(\mathrm{v}^{1}ight)^{2}$ where $\mathrm{v}^{1}$ is the velocity on reaching the bottom of the plane.\ $	herefore \mathrm{m}\left(\mathrm{v}^{1}ight)^{2}=\mathrm{mgh}-----(2)$\ Equating (1) and (2)\ $\mathrm{m}\left(\mathrm{v}^{1}ight)^{2}=\frac{\frac{1}{2}}{2} \mathrm{mv}^{2}$\ $\mathrm{v}^{1}=$\