Angular Momentum Questions

The Sun rotates around its centre once in $27$ days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass $m$ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period:

Assertion: For a system of particles under central force field, the total angular momentum is conserved.Reason: The torque acting on such a system is zero.

A particle of mass $m$ moves in the $XY$ plane with a velocity $v$ along the straight line $AB$. If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$, then:

A thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$. If two objects each of mass $m$ be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

A circular platform is mounted on a frictionless vertical axle. Its radius $R=2\text{m}$ and its moment of inertia $I=200{\text{kg m}}^2$. It is initially at rest. A $50\text{kg}$ man stands on the edge and begins to walk along the edge at a speed of $1{\text{ms}}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is:

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along: