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 . . . . . .$kg \,m^2$.

What are the factors on which the magnitude of the moment of inertia depends?

Let the moment of inertia of a hollow cylinder of length $30\, cm$ (inner radius $r = 10\, cm$ and outer radius $R = 20\, cm$),about its axis be $I$. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $I$,is ......... $cm$.

Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

$A$ swimmer curls their body before diving into the water from a height so that:

The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through its centre and perpendicular to it is $\frac{1}{12} ML^2$. The rod is bent in the middle so that the two halves make an angle of $60^o$. The moment of inertia of the bent rod about the same axis (passing through the original centre of the rod) would be: