$A$ uniform rod of length $l$ and density $\rho$ is revolving about a vertical axis passing through its one end. If $\omega$ is the angular velocity of the rod,then the centrifugal force per unit area of the rod is

$A$ ring starting from rest rotates under a constant angular acceleration of $8 \ rad \ s^{-2}$ due to an applied torque. How many revolutions will the ring complete in $5 \ s$? How many revolutions will it complete in the $6^{th}$ second? If the torque becomes zero after $6 \ s$,how many revolutions will the ring complete in the $7^{th}$ second?

Find the increase in the moment of inertia $I$ of a uniform rod (coefficient of linear expansion $\alpha$) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.

If the earth suddenly stops revolving and all its rotational $KE$ is used up in raising its temperature and if $s$ is taken to be the specific heat of the earth's material,the rise of temperature of the earth will be: ($R =$ radius of the earth and $\omega =$ its angular velocity,$J =$ Joule's constant)

$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid-point elastically. If the particle comes to rest after the collision,find the value of $M/m$.

$A$ particle performs uniform circular motion with an angular momentum $L$. If the angular frequency of the particle is doubled and its kinetic energy is halved,what will be its new angular momentum?