$A$ solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder $(a_c)$ to that of the sphere $(a_s)$ is

$A$ solid cylinder rolls without slipping down an inclined plane of height $h$. The velocity of the cylinder when it reaches the bottom is

Suppose a body of mass $M$ and radius $R$ is allowed to roll on an inclined plane without slipping from its topmost point $A$ at a height $h$. The velocity acquired by the body,as it reaches the bottom of the inclined plane,is given by $\beta = 1 + \frac{I}{MR^2}$. Find the expression for the velocity $v$.

$A$ sphere of mass $m$ and radius $r$ rolls on a horizontal plane without slipping with the speed $u$. Now if it rolls up an incline, the maximum height it would attain will be

$Assertion$ : The velocity of a body at the bottom of an inclined plane of given height is more when it slides down the plane,compared to when it rolls down the same plane.
$Reason$ : In rolling down,a body acquires both kinetic energy of translation and rotation.

From an inclined plane,a sphere,a disc,a ring,and a shell are rolled without slipping. The order of their reaching the base will be: