$A$ 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 .......... $m/s$. $(\sin 35^{\circ} = 0.57)$

How is the motion of a rolling sphere down a slope? Write the general formula for the kinetic energy of a rolling body down a slope.

$A$ sphere of radius $a$ and mass $m$ rolls along a horizontal plane with constant speed $v_{0}$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping,how far up the sphere will travel?

$A$ solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
$(a)$ Will it reach the bottom with the same speed in each case?
$(b)$ Will it take longer to roll down one plane than the other?
$(c)$ If so,which one and why?

$A$ hollow cylinder and a solid cylinder, initially at rest at the top of an inclined plane, are rolling down without slipping. If the time taken by the hollow cylinder to reach the bottom of the inclined plane is $2 \ s$, the time taken by the solid cylinder to reach the bottom of the inclined plane is: (in $s$)

Derive expressions for the kinetic energy and velocity of a body rolling without sliding down an inclined plane of inclination $\theta$.