The moment of inertia of a sphere of mass $M$ and radius $R$ is $I$. If the mass is kept constant,what will be the nature of the graph between $I$ and $R$?

$A$ heavy rod of weight $W$ is held in a horizontal position by two men at its ends. If one man suddenly lets go,what force will the other man feel?

$A$ thin uniform rod of length $L$ and mass $M$ is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of [where $g$ is gravitational acceleration]:

$A$ block of mass $m$ is attached to a pulley disc of equal mass $m$ and radius $r$ by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of $5\, m/s$. Its velocity when the string becomes taut will be

$A$ thin hollow cylinder slides with velocity $v$ without rotating. It then rolls without slipping with the same velocity $v$. Find the ratio of the kinetic energies in the two cases.

$A$ rod of mass $m$ and length $l$ is hinged at one end to a horizontal floor and stands vertically. If it is allowed to fall,the velocity with which its upper end strikes the floor is: