$A$ 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

$A$ uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly,what happens to its speed of rotation?

Three particles,each of mass $m$,are placed at the corners of an equilateral triangle of side $l$. Which of the following is/are correct?

Which of the following statements are correct?

$A$ hemisphere of mass $3m$ and radius $R$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity,find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\theta$,when the velocity of the hemisphere is $v$.

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring $= m$,radius $= r$)