Four particles, each of mass $$1$$ kg are placed at four corners of a square of side $$2$$ m. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______ kg m$$^2$$.

Four particles each of mass 1 kg at corners of a square with side 2 m. The axis passes through one vertex, perpendicular to the plane.

Taking the vertex through which the axis passes as origin, the distances of the four particles from the axis are:

- Particle at the vertex: $$r_1 = 0$$

- Two adjacent particles: $$r_2 = r_3 = 2$$ m (side length)

- Diagonally opposite particle: $$r_4 = 2\sqrt{2}$$ m (diagonal)

$$I = m(r_1^2 + r_2^2 + r_3^2 + r_4^2) = 1(0 + 4 + 4 + 8) = 16 \text{ kg m}^2$$

The answer is $$\boxed{16}$$ kg m$$^2$$.