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

$A$ body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity $V$. If the same body is a ring which rolls down the same inclined plane,then the linear velocity at the bottom of the plane is:

$A$ solid sphere,a disc,and a solid cylinder,all of the same mass and made of the same material,are allowed to roll down from rest on an inclined plane. Then,which of the following is true?

Prove that the velocity $v$ of translation of a rolling body (like a ring,disc,cylinder,or sphere) at the bottom of an inclined plane of height $h$ is given by $v^{2} = \frac{2gh}{1 + k^{2}/R^{2}}$ using dynamical considerations (i.e.,by considering forces and torques). Note: $k$ is the radius of gyration of the body about its symmetry axis,and $R$ is the radius of the body. The body starts from rest at the top of the plane.

$A$ solid sphere of mass $m$ and radius $R$ is released from rest on a sufficiently rough long inclined plane of inclination $\theta$ . Consider four points $A$,$B$,$C$ and $D$ on the sphere as shown in the figure. After one revolution,which of the following statements is correct regarding the acceleration of these points?

$A$ solid sphere rolls down without slipping on an inclined plane,then the percentage of rotational kinetic energy of the total energy will be ........ $\%.$