Two rings of the same material have radii $R$ and $nR$ respectively. The ratio of their moments of inertia about an axis passing through their centers and perpendicular to their planes is $1 : 8$. The value of $n$ is:

$A$ circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from an iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is:

$A$ rod of linear mass density $\lambda$ and length $L$ is bent to form a ring of radius $R$. The moment of inertia of the ring about any of its diameters is:

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

Three thin rods,each of mass $2M$ 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 $x$-axis is:

From a uniform wire,two circular loops are made: $(i)\ P$ of radius $r$ and $(ii)\ Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its center and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).