$A$ sphere of mass $50\,g$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/s$. Its total kinetic energy is

For a rolling spherical shell,the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ................

$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface with an angular speed $\omega$. The angular momentum of the disc about the origin $O$ is:

$A$ solid sphere with a velocity (of centre of mass) $v$ and angular velocity $\omega$ is gently placed on a rough horizontal surface. The frictional force on the sphere:

Consider a point $P$ at the contact point of a wheel on the ground,which rolls on the ground without slipping. Find the displacement of point $P$ when the wheel completes half of a rotation (given the radius of the wheel is $1 \ m$).

$A$ disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/s$. Its rotational kinetic energy is (in $,J$)