If a solid sphere is rolling without slipping on a horizontal plane,then the ratio of its rotational and total kinetic energies is

$A$ solid sphere of mass $500 \ g$ and radius $10 \ cm$ rolls without slipping with a velocity of $20 \ cm/s$. The total kinetic energy of the sphere will be ........ $J$.

Find the displacement of the point of contact with the ground when a ring of radius $R$ completes a half-rotation.

$A$ disc of radius $R$ is rotating with an angular velocity $\omega_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is $\mu_k$.
$(a)$ What was the velocity of its centre of mass before being brought in contact with the table?
$(b)$ What happens to the linear velocity of a point on its rim when placed in contact with the table?
$(c)$ What happens to the linear speed of the centre of mass when the disc is placed in contact with the table?
$(d)$ Which force is responsible for the effects in $(b)$ and $(c)$?
$(e)$ What condition should be satisfied for rolling to begin?
$(f)$ Calculate the time taken for the rolling to begin.

$A$ solid homogeneous sphere is rolling with sliding on a horizontal rough surface. For this type of motion of the sphere:

$A$ wheel of a bullock cart is rolling on a level road as shown in the figure. If its linear speed is $v$ in the direction shown,which one of the following options is correct ($P$ and $Q$ are the highest and lowest points on the wheel,respectively)?