$A$ solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is ...

$A$ solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane of height $h$. The angular velocity of the cylinder when it reaches the bottom of the plane will be

$A$ disc of mass $m$ and radius $r$ rolls down an inclined plane of height $h$. When it reaches the bottom of the plane,its rotational kinetic energy is ($g=$ acceleration due to gravity).

$A$ 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 $(x+y)_{min}$.

$A$ spherical shell and a solid cylinder of the same radius roll down an inclined plane. The ratio of their accelerations is ..........

$A$ solid cylinder $30\ cm$ in diameter at the top of an inclined plane $2.0\ m$ high is released and rolls down the incline without loss of energy due to friction. Its linear speed at the bottom is.......... $m/s$.