Starting from rest,at the same time,a ring,a coin (disc),and a solid ball of the same mass roll down an incline without slipping. The ratio of their translational kinetic energies at the bottom will be:

$A$ uniform spherical object of mass $M$ and radius $R$ has a moment of inertia $I$. It rolls without slipping down an inclined plane of angle $\theta$. What is its acceleration?

$A$ solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \ m/s$ at the bottom of the inclination. How far will the ball go up the plane (in $cm$)? (Use $g=10 \ m/s^2$)

$A$ hollow sphere of mass $m$ filled with a non-viscous liquid of same mass $m$ is released on a slope inclined at angle $\theta$ with the horizontal. The friction between the sphere and the slope is sufficient to prevent sliding,and frictional forces between the inner surface of the sphere and the liquid are negligible. After descending a certain height,the ratio of translational and rotational kinetic energies is found to be $x:y$. Find the numerical value of the expression $(x+y)_{min}$.

$A$ small sphere rolls without slipping from the top of a vertical track. The track has an inclined part and a horizontal part. The horizontal part is $1.0 \ m$ above the ground,and the top of the track is $2.4 \ m$ above the ground. The sphere falls to the ground at point $E$. The horizontal distance from the point directly below $C$ to point $E$ is $R$. Find the value of $R$ in meters.

$A$ thin metal disc of radius $0.25\,m$ and mass $2\,kg$ starts from rest and rolls down an inclined plane. If its rotational kinetic energy is $4\,J$ at the foot of the inclined plane,then the linear velocity (in $m/s$) at the same point is: