$A$ wheel of radius $1 \text{ m}$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

$A$ ring and a disc roll on a horizontal surface without slipping with the same linear velocity. If both have the same mass and the total kinetic energy of the ring is $4 \ J$,then the total kinetic energy of the disc is: (in $J$)

$A$ 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)?

Two identical circular loops are moving with the same kinetic energy; one rolls and the other slides. The ratio of their speed is:

$A$ sphere rolls without slipping. The radius of gyration about an axis passing through its center of mass is $K$. If the radius of the sphere is $R$,what fraction of the total energy is in the form of rotational kinetic energy?

$A$ thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic energy is