$A$ uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down an inclined plane,inclined at an angle $45^o$ to the horizontal. Find the minimum magnitude of the frictional coefficient required for rolling without slipping.

$A$ solid sphere rolling without friction on a horizontal surface with a constant speed of $2 \,m/s$, rolls up on an inclined ramp which is inclined at $30^{\circ}$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $g=10 \,m/s^2, \sin 30^{\circ}=1/2$) (in $\,m$)

$A$ solid sphere rolls down an inclined plane and its velocity at the bottom is $v_1$. Then the same sphere slides down the plane (without friction) and let its velocity at the bottom be $v_2$. Which of the following relations is correct?

$A$ cylinder is pure rolling up an incline plane. It stops momentarily and then rolls back. The force of friction

$A$ solid sphere,a solid cylinder,a disc,and a ring are rolling down an inclined plane. Which of these bodies will reach the bottom simultaneously?

$A$ solid cylinder of mass $M$ and radius $R$ rolls down a smooth inclined plane about its own axis and reaches the bottom with velocity $v$. What is the height of the inclined plane? (Assume $g$ is the acceleration due to gravity.)