Three balls of masses $2 \,kg$,$4 \,kg$,and $6 \,kg$ are placed at the midpoints of the sides of an equilateral triangle of side length $2 \,m$. The moment of inertia of the system about an axis passing through the centroid and perpendicular to the plane of the triangle is . . . . . .$kg \,m^2$.

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?

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

Two rings have their masses in ratio $1 : 2$ and their diameters are in the ratio $2 : 1$. The ratio of their moments of inertia is

Let $l$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to:

The moment of inertia of a circular ring of radius $r$ and mass $M$ about its diameter is: