$A$ 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

$A$ circular disc of mass $2 \,kg$ and radius $10 \,cm$ rolls without slipping with a speed $2 \,m/s$. The total kinetic energy of the disc is .......... $J$.

$A$ sphere is rolling without slipping on a fixed horizontal plane surface. In the figure,$A$ is the point of contact,$B$ is the centre of the sphere,and $C$ is its topmost point. Then:
$(i) \vec{V}_C - \vec{V}_A = 2(\vec{V}_B - \vec{V}_C)$
$(ii) \vec{V}_C - \vec{V}_B = \vec{V}_B - \vec{V}_A$
$(iii) |\vec{V}_C - \vec{V}_A| = 2|\vec{V}_B - \vec{V}_C|$
$(iv) |\vec{V}_C - \vec{V}_A| = 4|\vec{V}_B|$

$A$ 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?

In a bicycle,the radius of the rear wheel is twice the radius of the front wheel. If $r_F$ and $r_r$ are the radii,and $v_F$ and $v_r$ are the speeds of the topmost points of the wheels respectively,then:

$A$ solid sphere with a velocity (of centre of mass) $v$ and angular velocity $\omega$ is gently placed on a rough horizontal surface. The frictional force on the sphere: