Three particles of mass $m$ each are placed at the three vertices of an equilateral triangle. The length of each side of the triangle is $a$. The moment of inertia of this system about any side of the triangle is:

The moment of inertia $(M.I.)$ of four bodies,having the same mass $M$ and radius $R$,are reported as follows:
$I_{1} = M.I.$ of a thin circular ring about its diameter.
$I_{2} = M.I.$ of a circular disc about an axis perpendicular to the disc and passing through the centre.
$I_{3} = M.I.$ of a solid cylinder about its axis.
$I_{4} = M.I.$ of a solid sphere about its diameter.
Then:

$A$ wire of length $l$ and mass $m$ is bent in the form of a rectangle $ABCD$ with $(AB/BC) = 2$. The moment of inertia of this wire about the side $BC$ is

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

If $I_1$ is the moment of inertia of a thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its centre of mass,and $I_2$ is the moment of inertia of the ring formed by bending the rod about an axis passing through its centre and perpendicular to its plane,then:

$A$ 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: