$A$ thin rod of mass $M$ and length $L$ is bent at its midpoint $A$ such that it forms an angle of $60^{\circ}$. What is the moment of inertia about an axis passing through the midpoint $A$ and perpendicular to the plane of the rod?

Four point masses (each of mass $m$) are arranged in the $X-Y$ plane at coordinates $(a, 0)$,$(0, a)$,$(-a, 0)$,and $(0, 2a)$. What is the moment of inertia of this system about the $Y$-axis?

Two circular discs $A$ and $B$ are of equal masses and thickness but made of metals with densities ${d_A}$ and ${d_B}$ $({d_A} > {d_B})$. If their moments of inertia about an axis passing through their centres and normal to the circular faces are ${I_A}$ and ${I_B}$ respectively,then:

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_{c}$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_c: K_d$ 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 centre 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 $nr$). (in $\sqrt{2}$)

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is: