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 .......... $m$.

$A$ solid homogeneous sphere is rolling with sliding on a horizontal rough surface. For this type of motion of the sphere:

$Assertion$: $A$ rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of the lowest point on the disc is zero.
$Reason$: For a rigid disc rolling without slipping on a fixed rough horizontal surface,the velocity of the lowest point on the disc is always zero.

$A$ wheel of a bullock cart is rolling on a level road as shown in the figure. If its linear speed is $v$ in the direction shown,which one of the following options is correct ($P$ and $Q$ are the highest and lowest points on the wheel,respectively)?

$A$ solid sphere is moving on a horizontal plane. The ratio of its translational kinetic energy to its rotational kinetic energy is:

$A$ solid sphere of mass $1$ kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}$ $J$. The speed of the center of mass of the sphere in cm s$^{-1}$ is