$A$ ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is $K$. If the radius of the ball is $R$,then the fraction of total energy associated with its rotational energy is:

$A$ 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

In a bicycle,the radius of the rear wheel is twice the radius of the front wheel. If $r_F$ and $r_r$ are the radii,and $v_F$ and $v_r$ are the speeds of the topmost points of the wheels respectively,then:

$A$ solid sphere is moving on a horizontal plane. The ratio of its translational kinetic energy to its rotational kinetic energy is:

$A$ wheel of radius $R$ rolls on the ground with a uniform velocity $v$. The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

For a rolling body,the velocities of points $P_1$ and $P_2$ are ${\vec v_1}$ and ${\vec v_2}$,respectively. Which of the following is correct?