In the above problem, the final angular velocity of the small cylinder is

The portion $AB$ of the wedge shown in figure is rough and $BC$ is smooth. A solid cylinder rolls without slipping from $A$ to $B$. The ratio of translational kinetic energy to rotational kinetic energy when the cylinder reaches point $C$ is,

In the figure shown mass of both, the spherical body and block is $m$. Moment of inertia of the spherical body about centre of mass is $2m{R}^2$. The spherical body rolls on the horizontal surface. There is no slipping at any surfaces in contact. The ratio of kinetic energy of the spherical body to that of block is

A cylinder executes pure rolling without slipping with a constant velocity on a plank, whose upper surface is rough enough, but lower surface is smooth. The plank is kept at rest on a smooth horizontal surface by the application of an external force $F$. Choose the correct alternative.