$A$ hollow sphere of mass $2 \, kg$ and diameter $0.2 \, m$ is rolling on an inclined plane with a velocity of $0.5 \, m/s$. The kinetic energy of the sphere will be .......... $J$.

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:

Explain why friction is necessary to make the disc in the figure roll in the direction indicated.
$(a)$ Give the direction of frictional force at $B$,and the sense of frictional torque,before perfect rolling begins.
$(b)$ What is the force of friction after perfect rolling begins?

Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc,the distance through which $P$ moves in one full rotation of the disc is:

The ratio of kinetic energies of two spheres rolling with equal centre of mass velocities is $2 : 1$. If their radii are in the ratio $2 : 1$,then the ratio of their masses will be

$A$ disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in the figure. At any instant,for the lowermost point of the disc -