$A$ ball is rolling without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $K$. If the radius of the ball is $R$,what fraction of the total energy is rotational kinetic energy?

$A$ spherical object of mass $M$ and radius $R$ has a moment of inertia $I$ about its axis. If this object rolls down an inclined plane of angle $\theta$ without slipping,its acceleration is given by:

$A$ ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle $60^{\circ}$ with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $(2-\sqrt{3}) / \sqrt{10} \,s$, then the height of the top of the inclined plane, in metres, is. . . . . . Take $g=10 \,m \,s^{-2}$.

$A$ uniform disk of mass $m$ and radius $R$ rolls without slipping down an inclined plane of length $l$ and inclination $\theta$. Initially,the disk was at rest at the top of the inclined plane. Its angular momentum about the point of contact with the inclined plane when it reaches the bottom will be equal to:

Consider a situation in which a ring,a solid cylinder,and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and have identical diameters. The correct statement for this situation is:

$A$ solid cylinder of mass $2 \; kg$ and radius $50 \; cm$ rolls up an inclined plane of angle of inclination $30^{\circ}$. The centre of mass of the cylinder has a speed of $4 \; m/s$. The distance travelled by the cylinder on the inclined surface will be ...... $m$.