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

$A$ disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total kinetic energy is

$A$ solid sphere spinning about a horizontal axis with an angular velocity $\omega$ is placed on a horizontal surface. Subsequently,it rolls without slipping with an angular velocity of

The centre of a wheel rolling on a plane surface moves with a speed $v_{0}$. $A$ particle on the rim of the wheel at the same level as the centre will be moving at a speed $\sqrt{x} \, v_{0}$. Then the value of $x$ is ...... .

$A$ solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity $v_{0}$. When it finally starts rolling without slipping, the speed of its centre is

$A$ solid sphere of mass $2 \ kg$ is rolling on a frictionless horizontal surface with velocity $6 \ m \ s^{-1}$. It collides with the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring $= 36 \ N \ m^{-1}$). (in $m$)