Three thin rods,each of mass $M$ and length $L$,are placed along the $X$,$Y$,and $Z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $Z$ axis is:

Two rods of equal length $(l)$ and equal mass $M$ are kept along the $x$ and $y$ axes respectively,such that their center of mass lies at the origin. The moment of inertia about the line $y = x$ is ...........

Two rings have their moments of inertia in the ratio $4 : 1$ and their diameters are in the ratio $4 : 1$. The ratio of their masses is

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ are made respectively from a uniform wire. The moment of inertia of loop $Q$ about its axis is $4$ times that of loop $P$ about its axis. The value of $n$ is:

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: