$A$ rigid body can be hinged about any point on the $x$-axis. When it is hinged such that the hinge is at $x$,the moment of inertia is given by $I = 2x^2 - 12x + 27$. The $x$-coordinate of the centre of mass is:

$A$ uniform thin bar of mass $6 \,kg$ and length $2.4 \,m$ is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is ...... $\times 10^{-1} \,kg \cdot m^2$.

Consider the following statements:
Assertion $(A)$: The moment of inertia of a rigid body reduces to its minimum value as compared to any other parallel axis when the axis of rotation passes through its centre of mass.
Reason $(R)$: The weight of a rigid body always acts through its centre of mass in a uniform gravitational field.
Of these statements:

The radius of gyration of a circular disc of radius $R$ and mass $m$ rotating about its diameter as an axis is:

The moment of inertia of a uniform rod of mass $M$ and length $L$ about an axis passing through its center and perpendicular to it is $\frac{1}{12} ML^2$. The rod is bent at the center such that the two halves make an angle of $60^\circ$ with each other. Find the moment of inertia of the bent rod about the same axis passing through the center of the rod (the point of bending) and perpendicular to the plane containing the two halves.

Four spheres of diameter $2a$ and mass $M$ are placed with their centers on the four corners of a square of side $b$. The moment of inertia of the system about an axis along one of the sides of the square is