$A$ thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is $6 \ J$,then the total kinetic energy of the ring is (in $J$)

An object of mass $10 \ kg$ and radius $0.5 \ m$ is rolling without slipping with a velocity of $2 \ m/s$. Its total kinetic energy is $32.8 \ J$. The radius of gyration of the object is .......... $m$.

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 $1 \ m$).

Consider a point $P$ on the circumference of a disc of radius $R$ rolling along a horizontal surface. The distance traveled by point $P$ in one full rotation of the disc is:

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

$A$ uniform disc of mass $0.5\,kg$ and radius $r$ is projected with velocity $18\,m/s$ at $t = 0\,s$ on a rough horizontal surface. It starts off with a purely sliding motion at $t = 0\,s$. After $2\,s$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2\,s$ will be $..............J$ (given,coefficient of friction is $0.3$ and $g = 10\,m/s^2$).