The three rods $A$,$B$,and $C$ shown in the figure have the same length $L$ and the same mass $M$. If the system rotates such that rod $B$ acts as the axis of rotation,what will be the moment of inertia of the system?

The ratios of the masses and radii of two circular rings are $1:2$ and $2:1$ respectively. What is the ratio of their moments of inertia?

$A$ massless equilateral triangle $EFG$ of side $'a'$ (as shown in the figure) has three particles of mass $m$ situated at its vertices. The moment of inertia of the system about the line $EX$ perpendicular to $EG$ in the plane of $EFG$ is $\frac{N}{20} ma^{2}$,where $N$ is an integer. The value of $N$ is

Four point masses,each of mass $m$,are fixed at the corners of a square of side $\ell$. The square is rotating with angular frequency $\omega$,about an axis passing through one of the corners of the square and parallel to its diagonal,as shown in the figure. The angular momentum of the square about this axis is $.......m\ell^2 \omega$.

$A$ circular disc of radius $R$ and thickness $R/8$ has a moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about an axis passing through its diameter 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: