$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$. Two particles each of mass $m$ are now attached at diametrically opposite points. The angular speed of the ring will become

The angular momentum of a system of particles is not conserved:

$A$ swimmer,while jumping into a river from a height,easily forms a loop in the air if:

If the Earth were to suddenly contract to $\frac{1}{n}$ th of its present radius without any change in its mass, the duration of the new day will be nearly

$A$ smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size,each of mass $m$,which can slide freely along the rod. Initially,the two beads are at the center of the rod and the system is rotating with angular velocity $\omega_0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external torques. When the beads reach the ends of the rod,the angular velocity of the system is:

$A$ rigid body of mass $2 \ kg$ is moving in a circular path of radius $0.8 \ m$ with an angular velocity of $44 \ rad \ s^{-1}$. If the radius of the circular path becomes $1 \ m$,the new angular velocity of the body will be ........ $rad \ s^{-1}$.