The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1, I_2, I_3$ and $I_4$,respectively (the square $ABCD$ circumscribes the circle). The distance of the centre of mass of the disc from its geometrical centre is given by

For a rectangle $ABCD$ with $BC = 2AB$,about which axis will the moment of inertia be minimum?

An annular ring has mass $10 \ kg$ and inner and outer radii are $5 \ m$ and $10 \ m$ respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

Consider the following statements:
Assertion $(A)$: The moment of inertia of a rigid body reduces to its minimum value as compared to any other parallel axis when the axis of rotation passes through its centre of mass.
Reason $(R)$: The weight of a rigid body always acts through its centre of mass in a uniform gravitational field.
Of these statements:

Three point masses $m$ are placed at the corners of an equilateral triangle of side length $\ell$. What is the moment of inertia of the system about an axis passing through one side of the triangle?