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

Three particles are connected by massless rods lying along the $y-$ axis. If the system rotates about the $x-$ axis with an angular speed of $2 \, rad/s$,the moment of inertia $(M.I.)$ of the system is ......... $kg \cdot m^2$.

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.

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 $nr$).

Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is:

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively,and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $\frac{r_2}{r_1}$ equals: