$A$ person is sitting on a rotating stool with their arms outstretched. Suddenly, they fold their arms inward.

$A$ particle is moving in a circular path. Which of the following statements is true?

$A$ 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 $?$

$A$ thin circular ring of mass $M$ and radius $r$ is rotating with a constant angular velocity $\omega$. Two particles,each of mass $m$,are attached to the opposite ends of a diameter of the ring. The new angular velocity of the ring will be:

Due to global warming, if the ice in the polar region melts and some of this water flows to the equatorial region, then

Suppose all the people in the world line up at the equator and all start running at speed $v_{rel}$ relative to the surface of the Earth along the equatorial circle. The initial angular velocity of the Earth is $\omega_0$. Let the moment of inertia of the Earth be $I_E$,the moment of inertia of all people be $I_P$,and the radius of the Earth be $R$. Which of the following statements is correct?