Two cylinders having radii $2R$ and $R$ and moment of inertia $4I$ and $I$ about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity ${\omega }_0.$ The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite directions. During this

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.