$A$ loop rolls down on an inclined plane. The fraction of its total kinetic energy that is associated with the rotational motion is

The rotational kinetic energy of a solid sphere of mass $3 \; kg$ and radius $0.2 \; m$ rolling down an inclined plane of height $7 \; m$ is (in $; J$)

$A$ cylinder rolls up an inclined plane to a certain height and then rolls down. (It does not slip during the entire motion.) What is the direction of the frictional force acting on the cylinder?

$A$ solid sphere (mass $2M$) and a thin hollow spherical shell (mass $M$) both of the same size,roll down an inclined plane,then

$A$ sphere of mass $2 \, kg$ and radius $0.5 \, m$ is rolling with an initial speed of $1 \, m/s$ up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane,without slipping. How long will the sphere take to return to the starting point $A$? (in seconds)

$A$ thick-walled hollow sphere has outside radius $R_0$. It rolls down an incline without slipping and its speed at the bottom is $v_0$. Now the incline is waxed,so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be $5v_0/4$. The radius of gyration of the hollow sphere about an axis through its centre is