$A$ solid cylinder is rolling down on an inclined plane of angle $\theta$. The coefficient of static friction between the plane and the cylinder is $\mu_s$. The condition for the cylinder not to slip is

$A$ solid cylinder and a solid sphere of same mass and radius roll without slipping on a rough inclined plane. The force of friction is ..........

Two bodies,a ring and a solid cylinder of the same material,are rolling down without slipping an inclined plane. The radii of the bodies are the same. The ratio of the velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$. Then,the value of $x$ is .... .

$A$ solid uniform disk of mass $m$ rolls without slipping down a fixed inclined plane with an acceleration $a$. The frictional force on the disk due to the surface of the plane is:

$A$ disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

$A$ sphere of mass $m$ and radius $r$ rolls on a horizontal plane without slipping with the speed $u$. Now if it rolls up an incline, the maximum height it would attain will be