If the volume of the Earth suddenly shrinks to $1/64$ of its present volume without any change in its mass,then the duration of the day on Earth will be ..... hours.

$A$ uniform disc of mass $M$ and radius $R$ is rotating about a horizontal axis passing through its centre with angular velocity $\omega$. $A$ piece of mass $m$ breaks from the disc and flies off vertically upwards. The angular speed of the disc will be

$A$ stone of mass $m$,tied to the end of a string,is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually,keeping the angular momentum of the stone about the centre of the circle constant. Then,the tension in the string is given by $T = Ar^n$,where $A$ is a constant and $r$ is the instantaneous radius of the circle. The value of $n$ is equal to

$Assertion$ : For a system of particles under a central force field,the total angular momentum is conserved.
$Reason$ : The torque acting on such a system is zero.

What does not change in the field of a central force?

An ant is sitting on the edge of a rotating disc. If the ant walks along the diameter to reach the other end, how will the angular velocity of the disc change?