$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are gently placed at opposite ends of a diameter of the ring. The new angular velocity of the ring will be

$A$ 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:

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

$A$ swimmer can easily perform somersaults in the air while jumping from a height if he:

If the radius of the Earth becomes $1/n^{th}$ of its present value,without any change in its mass,then the duration of the day becomes:

$A$ thin uniform rod of mass $M$ and length $L$ is rotating about a perpendicular axis passing through its centre with a constant angular velocity $\omega$. Two objects,each of mass $\frac{M}{3}$,are attached gently to the two ends of the rod. The rod will now rotate with an angular velocity of