$A$ sphere is rolling without slipping on a fixed horizontal plane surface. $A$ is the point of contact,$B$ is the centre of the sphere,and $C$ is the topmost point. Then:

$A$ ring of mass $m$ is rolling without slipping with linear velocity $v$ as shown in the figure. $A$ rod of identical mass $m$ is fixed along one of its diameters. The total kinetic energy of the system is:

$A$ solid sphere of mass $1$ kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}$ $J$. The speed of the center of mass of the sphere in cm s$^{-1}$ is

$A$ spherical shell of $1 \, kg$ mass and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane (as shown in the figure). The magnitude of the angular momentum of the shell about the origin $O$ is $\frac{a}{3} R^{2} \omega$. The value of $a$ will be ..............

When a rolling body enters onto a smooth horizontal surface,it will ............

$A$ solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49 \text{ m/s}$, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is . . . . . . seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8 \text{ m/s}^2$)