$A$ solid sphere of mass $1 \ kg$ is rolling on a rough table with a linear speed of $1 \ m/s$. Its total kinetic energy is ....... $J$.

The centre of a wheel rolling on a plane surface moves with a speed $v_{0}$. $A$ particle on the rim of the wheel at the same level as the centre will be moving at a speed $\sqrt{x} \, v_{0}$. Then the value of $x$ is ...... .

$A$ boy is pushing a ring of mass $2 \ kg$ and radius $0.5 \ m$ with a stick as shown in the figure. The stick applies a force of $2 \ N$ on the ring and rolls it without slipping with an acceleration of $0.3 \ m/s^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs,and the coefficient of friction between the stick and the ring is $(P/10)$. The value of $P$ is

Two spheres are rolling with the same velocity (for their $C.M.$). Their ratio of kinetic energy is $2:1$ and the ratio of their radii is $2:1$. Their mass ratio will be:

$A$ hoop of radius $2 \; m$ weighs $100 \; kg$. It rolls along a horizontal floor so that its centre of mass has a speed of $20 \; cm/s$. How much work has to be done to stop it?

$A$ spherical ball is rolling on a table without slipping. What fraction of its total kinetic energy is associated with its rotational motion?