Three identical thin rods each of mass $m$ and length $l$ are placed along $x, y$ and $z$-axes respectively. They are placed such that one end of each rod is at the origin $O$. The moment of inertia of this system about the $z$-axis is:

Two discs of same mass and same thickness have densities $\rho_1$ and $\rho_2$. The ratio of their moment of inertia about their central axes is .........

$A$ circular disc is to be made by using iron and aluminium,so that it acquires a large moment of inertia about its geometrical axis. This is possible with:

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:

Of the two eggs which have identical sizes,shapes and weights,one is raw and the other is half-boiled. The ratio between the moment of inertia of the raw egg to the half-boiled egg about their central axis is

Four particles,each of mass $1 \ kg$,are placed at the four corners of a square of side $2 \ m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertices is . . . . . . $kg \ m^2$.