$A$ particle on the outer surface of a wheel,which is initially at rest,is in contact with the ground at point $P$. Find the displacement of this particle when the wheel completes half a rotation in the forward direction. (Radius of the wheel $= 5 \ m$)

$A$ uniform non-deformable cylinder of mass $m$ and radius $R$ is rolling without slipping on a horizontal rough surface. The force of friction is

$A$ solid sphere is in rolling motion. In rolling motion,a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

$A$ solid sphere of mass $2 \ kg$ and radius $0.5 \ m$ is rolling without slipping on a horizontal surface. The ratio of the rotational and translational kinetic energies of the sphere is (in $: 5$)

$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300 \, J$. The translational kinetic energy of the disc is:

$A$ solid sphere and a solid cylinder, each of mass $M$ and radius $R$, are rolling with a linear speed $v$ on a flat surface without slipping. Let $L_1$ be the magnitude of the angular momentum of the sphere with respect to a fixed point $O$ on the surface along the path of the sphere. Likewise, let $L_2$ be the magnitude of the angular momentum of the cylinder with respect to the same fixed point $O$ along its path. The ratio $\frac{L_1}{L_2}$ is