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:

$A$ solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity $v_{0}$. When it finally starts rolling without slipping, the speed of its centre is

$A$ solid sphere and a solid cylinder, each of mass $M$ and radius $R$, are rolling with a linear speed $v$ on a flat surface without slipping. Let $L_1$ be the magnitude of the angular momentum of the sphere with respect to a fixed point $O$ on the surface along the path of the sphere. Likewise, let $L_2$ be the magnitude of the angular momentum of the cylinder with respect to the same fixed point $O$ along its path. The ratio $\frac{L_1}{L_2}$ is

$A$ thin hollow cylinder,open at both ends,slides without rotating and then rolls without slipping with the same speed. The ratio of kinetic energies in the two cases will be:

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

$A$ ring and a disc roll on a horizontal surface without slipping with the same linear velocity. If both have the same mass and the total kinetic energy of the ring is $4 \ J$,then the total kinetic energy of the disc is: (in $J$)