Three thin uniform rods,each of mass $M$ and length $L$,are placed along the three Cartesian axes such that one end of each rod is at the origin. Find the moment of inertia of this system about the $z$-axis.

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio $1 : 3$. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio:

Moment of inertia of a solid sphere about its diameter is $I$. It is then casted into $27$ small spheres of same diameter. The moment of inertia of each new sphere is

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

Point masses of $1, 2, 3,$ and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0),$ and $(-2, -2, 0)$ respectively. What is the moment of inertia of this system about the $x$-axis in $kg-m^2$?

Four spheres of diameter $2a$ and mass $M$ are placed with their centers on the four corners of a square of side $b$. The moment of inertia of the system about an axis along one of the sides of the square is