When a body is rolling without slipping on a rough horizontal surface,the work done by friction is ........

Find the displacement of the point of contact with the ground when a ring of radius $R$ completes a half-rotation.

$A$ 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

$A$ wheel of a bullock cart is rolling on a level road as shown in the figure. If its linear speed is $v$ in the direction shown,which one of the following options is correct ($P$ and $Q$ are the highest and lowest points on the wheel,respectively)?

$A$ 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?

$A$ boy is pushing a ring of mass $2 \ kg$ and radius $0.5 \ m$ with a stick as shown in the figure. The stick applies a force of $2 \ N$ on the ring and rolls it without slipping with an acceleration of $0.3 \ m/s^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs,and the coefficient of friction between the stick and the ring is $(P/10)$. The value of $P$ is