$A$ solid sphere is rotating in free space. If the radius of the sphere is increased while keeping its mass constant,which of the following quantities will remain unaffected?

$A$ person is rotating on a rotating table with an angular speed of $\omega$. He holds two identical masses in his outstretched hands. Without moving his hands,he simply drops the masses. How will his angular velocity change?

$A$ 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 ........ $rad/s$.

State the law of conservation of angular momentum and explain it with the example of a girl sitting on a swivel chair.

$A$ horizontal disc of moment of inertia $4.25 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning counter-clockwise at $15 \,rps$ about its axis,as viewed from above. $A$ second disc of moment of inertia $1.80 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning clockwise at $25 \,rps$ as viewed from above about the same axis and is dropped on top of the first disc. The two discs stick together and rotate as one about their axis of symmetry. The new angular velocity of the system as viewed from above is close to

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