The angular momentum of a moving body remains constant if

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.

An equilateral triangle $ABC$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $AO$. Then the beads are released from rest simultaneously and allowed to slide down,one along $AB$ and the other along $AC$ as shown. Neglecting frictional effects,the quantities that are conserved as the beads slide down,are

$A$ disc of mass $M$ and radius $R$ is moving with an angular velocity $\omega$ as shown in the figure. Find the angular momentum of the disc about the reference point $O$.

$A$ rod of mass $m$ and length $l$ is placed on a smooth floor and pivoted at its centre. $A$ gun of mass $m$ (without a shot) is mounted at one end. It fires a shot of mass $\frac{m}{10}$ with velocity $v$ relative to the gun. The angular velocity of the rod will be:

$A$ circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two particles of mass $M$ are gently attached to the ring at the ends of a diameter. The ring will now rotate with an angular velocity $\omega'$ equal to: