Question

A solid sphere, a thin-walled hollow sphere, a solid cylinder, a thin-walled hollow cylinder and a ring, each of mass $m$ and radius $R$, are simultaneously released at rest from top of an inclined plane, as shown in figure. The objects roll down the plane without slipping. Also we may consider the objects and the surface on which they roll to be perfectly rigid. Match column I and II

Answer 1

As seen from the attached concept, $K{E}_{tot}$ is same for all the bodies.
MI of ring and hollow cylinder are same for a given mass m and radius R.
Hence, $K{E}_{rot}$ is same for both ring and hollow cylinder.
MI of $I_{solidcylinder}>I_{hollowsphere}>I_{solidsphere}$
$I_{ring}=I_{hollowcylinder}>I_{solidcylinder}>I_{hollowsphere}>I_{solidsphere}$
Hence, Rotational KE of the objects having the greater MI is more compared to others.
$\tau =I\alpha$
All objects are subjected to same torque. Object having least MI has the maximum angular acceleration.
Hence, solid sphere has the max angular acceleration.
Time taken to reach the bottom is maximum for
Ring or hollow cylinder.