$A$ heavy solid sphere is thrown on a horizontal rough surface with initial velocity $u$ without rolling. What will be its speed when it starts pure rolling motion?

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 is in rolling motion. In rolling motion,a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

$A$ disc is performing pure rolling on a surface. The positions of $P$ and $Q$ at an instant are shown in the figure. $C$ is the center of the disc. Which of the following is true for their velocities at the instant when $P$ and $Q$ are at the same distance from the center?

$A$ 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 $..........\,m/s$.

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: