$A$ solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '$a_{c}$' to that of sphere '$a_{s}$' is

$A$ 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?

State the necessary condition for a solid cylinder to roll without slipping down an inclined plane with friction.

$A$ small ring is rolling without slipping on the circumference of a large bowl as shown in the figure. The ring is moving down at $P_{1}$,comes down to the lowest point $P_{2}$,and is climbing up at $P_{3}$. Let $v_{CM}$ denote the velocity of the centre of mass of the ring. Choose the correct statement regarding the frictional force on the ring.

$A$ solid cylinder and a disc of same radii are allowed to roll down a rough inclined plane from the top of a plane. The ratio of their times taken to reach the bottom of the inclined plane is

$A$ 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: