The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______ m. Given, the length of the rod is $$10\sqrt{3} \text{ m}$$.

For a cylindrical rod (uniform rod) of length $$L$$, the moment of inertia about an axis perpendicular to its length and passing through its center is:

$$I = \frac{ML^2}{12}$$

The radius of gyration $$k$$ is defined by $$I = Mk^2$$, so:

$$Mk^2 = \frac{ML^2}{12}$$

$$k = \frac{L}{\sqrt{12}} = \frac{L}{2\sqrt{3}}$$

Given $$L = 10\sqrt{3} \text{ m}$$:

$$k = \frac{10\sqrt{3}}{2\sqrt{3}} = \frac{10}{2} = 5 \text{ m}$$

The radius of gyration is $$\textbf{5}$$ m.