$A$ sphere is rolling down an incline without slipping. If the height of the incline is $14 \ m$,find its linear velocity at the bottom.

$A$ ring,a solid sphere,and a disc are rolled down an inclined plane from the same height. The order in which they reach the bottom is:

$A$ solid sphere is rolling without slipping on a semi-circular track of radius $R = 10 \ m$ as shown in the figure. The radius of the solid sphere is much smaller than the radius of the semi-circular track. At the lowest point, it has a velocity $v = 10 \ m/s$. To what maximum angle $\theta$ from the vertical will the sphere travel before it comes back down? Neglect the rolling friction between the sphere and the track. (Take $g = 10 \ m/s^2$)

$A$ uniform solid cylinder of mass $m$ and radius $r$ rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane,then the linear acceleration of the cylinder axis will be:

$A$ solid sphere and a solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping throughout the motion. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h_{sph}}{h_{cyl}}$ is given by

$A$ ball of radius $11 \ cm$ and mass $8 \ kg$ rolls from rest down a ramp of length $2 \ m$. The ramp is inclined at $35^{\circ}$ to the horizontal. When the ball reaches the bottom,its velocity is .......... $m/s$. $(\sin 35^{\circ} = 0.57)$