$A$ disc is rotating with an angular speed of $\omega$. If a child sits on it,which of the following is conserved?

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:

$A$ rotating table has an angular velocity $\omega$ and a moment of inertia $I_1$. $A$ man of mass $m$ stands at the center of the table. If the man walks a distance $r$ along the radius of the table,what will be his final angular velocity?

$A$ thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of same dimensions but of mass $M/2$ is placed gently on the first disc co-axially,then the new angular velocity of the system is:

$A$ person standing on a rotating platform has his hands lowered. He suddenly outstretch his arms. The angular momentum

$A$ 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 $?$