$A$ uniform disc of mass $100 \ kg$ and radius $2 \ m$ is rotating at $1 \ rad/s$ about a perpendicular axis passing through its centre. $A$ boy of mass $60 \ kg$ standing at the centre of the disc suddenly jumps to a point which is $1 \ m$ from the centre of the disc. The final angular velocity of the boy (in $rad/s$) is

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

$A$ solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere $?$

$A$ 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:

$A$ hot solid sphere is rotating about a diameter at an angular velocity $\omega_0$. If it cools so that its radius reduces to $\frac{1}{\eta}$ of its original value,its angular velocity becomes .............

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