Point masses $1, 2, 3$ and $4 \text{ kg}$ are located at the points $(0,0,0), (2,0,0), (0,3,0)$ and $(-2,-2,0)$ respectively. The moment of inertia of this system about the $x$-axis will be: (in $\text{ kg m}^2$)

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

The moment of inertia of a uniform rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to it is $\frac{1}{12} ML^2$. The rod is bent at the center such that the two halves make an angle of $60^\circ$ with each other. Find the moment of inertia of the bent rod about the same axis passing through the center of the rod (the point of bending) and perpendicular to the plane containing the two halves.

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

$A$ system consists of two identical spheres,each of mass $1.5\, {kg}$ and radius $50\, {cm}$,attached to the ends of a light rod. The distance between the centers of the two spheres is $5\, {m}$. What is the moment of inertia of the system about an axis perpendicular to the rod and passing through its midpoint? (in ${kgm}^{2}$)

$A$ quarter circular sector is cut from a uniform circular disc. The mass of this sector is $M$. It is rotated about an axis passing through the center of the original disc and perpendicular to its plane. The moment of inertia of this sector about the axis of rotation is: