$A$ 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 $J$)

$A$ solid cylinder of mass $3 \, kg$ is rolling on a horizontal surface with velocity $4 \, m s^{-1}$. It collides with a horizontal spring of force constant $200 \, N m^{-1}$. The maximum compression produced in the spring will be ............... $m$.

$A$ 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

$A$ wheel of radius $2 \ cm$ is at rest on a horizontal surface. $A$ point $P$ on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface,the displacement of point $P$ after half a rotation of the wheel is:

What is the ratio of total kinetic energy to rotational kinetic energy for a rolling disc?

For a rolling spherical shell,the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ................