$A$ body is rolling on a horizontal surface without slipping. Its rotational kinetic energy is equal to its translational kinetic energy. The body is a:

$A$ uniform solid cylinder of mass $m$ and radius $R$ is set in rotation about its axis with an angular velocity $\omega_0$,then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and plane is equal to $\mu$. The time after which the cylinder starts rolling without slipping is

Consider a point $P$ on the circumference of a disc of radius $R$ rolling along a horizontal surface. The distance traveled by point $P$ in one full rotation of the disc is:

Two identical circular loops are moving with the same kinetic energy; one rolls and the other slides. The ratio of their speed is:

$A$ solid sphere of mass $2 \ kg$ is rolling on a frictionless horizontal surface with velocity $6 \ m \ s^{-1}$. It collides with the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring $= 36 \ N \ m^{-1}$). (in $m$)

$A$ cylinder rolls without slipping down an inclined plane. The number of degrees of freedom it has is: