If a solid sphere is rolling,the ratio of its rotational kinetic energy to the total kinetic energy is given by

Suppose a body of mass $M$ and radius $R$ is allowed to roll on an inclined plane without slipping from its topmost point $A$. The acceleration of the body down the plane is given by (where $\beta = 1 + \frac{I}{MR^2}$):

$A$ disc rolls without slipping on an inclined plane. What fraction of its total energy is in the form of rotational kinetic energy?

$A$ ring is rolling on an inclined plane. The ratio of the linear and rotational kinetic energies will be

$A$ 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?

$A$ solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of rolling friction in upward and downward motion respectively is ............