$A$ disc of radius $r$ is rotating about its centre with an angular speed $\omega_0$. It is gently placed on a rough horizontal surface. After what time will it be in pure rolling?

$A$ circular disc of mass $2 \,kg$ and radius $10 \,cm$ rolls without slipping with a speed $2 \,m/s$. The total kinetic energy of the disc is .......... $J$.

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:

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its centre and $Q$ and $P$ are two points on the same horizontal line passing through $C$,such that $Q$ is at a distance $r$ from $C$ and $P$ is at a distance $r$ from $C$ on the opposite side. Let $V_P, V_Q$ and $V_C$ be the magnitudes of velocities of points $P, Q$ and $C$ respectively,then:

$A$ solid disc and a ring,both of radius $10\; cm$,are placed on a horizontal table simultaneously,with an initial angular speed equal to $10\pi\; rad\; s^{-1}$. Which of the two will start to roll earlier? The coefficient of kinetic friction is $\mu_k = 0.2$.

$A$ solid sphere of mass $5 \,kg$ rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed $4 \,m/s$. (in $\,J$)