$A$ solid disc rolls clockwise without slipping over a horizontal path with a constant speed $v$. Then the magnitude of the velocities of points $A, B$ and $C$ (see figure) with respect to a standing observer are:

$A$ solid sphere with a velocity (of centre of mass) $v$ and angular velocity $\omega$ is gently placed on a rough horizontal surface. The frictional force on the sphere:

$A$ circular hoop of radius $50 \ cm$ and mass $1 \ kg$ rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let $v$ be the velocity of the centre of the hoop when it ceases to slip. The ratio $v / \omega_0$ will be (in $cm$)

$A$ solid sphere of mass $2 \ kg$ and radius $0.5 \ m$ is rolling without slipping on a horizontal surface. The ratio of the rotational and translational kinetic energies of the sphere is (in $: 5$)

$A$ solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of the centre of mass of the sphere will be $..........\,m/s$.

$A$ 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 ............... $m$.