$A$ sphere of mass $2 \, kg$ and radius $0.5 \, m$ is rolling with an initial speed of $1 \, m/s$ up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane,without slipping. How long will the sphere take to return to the starting point $A$? (in seconds)

$STATEMENT-1$: Two cylinders,one hollow (metal) and the other solid (wood) with the same mass and identical dimensions,are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
$STATEMENT-2$: By the principle of conservation of energy,the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

$A$ 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?

$A$ body starts rolling down an inclined plane of length $L$ and height $h$. This body reaches the bottom of the plane in time $t$. The relation between $L$ and $t$ is:

$A$ 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.

$A$ uniform ring of radius $R$ is moving on a horizontal surface with speed $v$,then climbs up a ramp of inclination $30^{\circ}$ to a height $h$. There is no slipping in the entire motion. Then,$h$ is