$A$ 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?

$A$ uniform sphere of radius $R$ and mass $m$ is placed on an inclined plane which makes an angle $45^{\circ}$ to the horizontal. For which of the following values of the coefficient of friction does the sphere roll without slipping? Select the incorrect option.

$A$ 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

$A$ body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity $V$. If the same body is a ring which rolls down the same inclined plane, then the linear velocity at the bottom of the plane is:

$A$ ring of radius $3a$ is fixed rigidly on a table. $A$ small ring of mass $m$ and radius $a$ rolls inside it without slipping,as shown in the figure. The small ring is released from position $A$ (the horizontal position). What will be the speed of the center of the small ring when it reaches the lowest point?

$A$ 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: