$A$ solid sphere is rolling on a frictionless surface,as shown in the figure,with a translational velocity $v \, m/s$. If it is to climb the inclined surface to a height $h$,then $v$ should be:

$A$ solid cylinder is suspended symmetrically by two massless strings,as shown in the figure. The distance the cylinder should fall by unbinding the strings to achieve a speed of $4\,ms^{-1}$ is $........cm$. (Take $g=10\,ms^{-2}$)

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

$A$ body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity $V$. If the same body is a ring which rolls down the same inclined plane,then the linear velocity at the bottom of the plane is:

$A$ solid cylinder $P$ rolls without slipping from rest down an inclined plane,attaining a speed $v_p$ at the bottom. Another smooth solid cylinder $Q$ of the same mass and dimensions slides without friction from rest down the inclined plane,attaining a speed $v_q$ at the bottom. The ratio of the speeds $\frac{v_q}{v_p}$ is

If a sphere is rolling,the ratio of its rotational energy to the total kinetic energy is given by