A circular disc of radius $b$ has a hole of radius $a$ at its centre. If the mass per unit area of the disc varies as $\frac{\sigma_0}{r}$ then, the radius of gyration of the disc about its axis passing through the center is\\
(1) $\frac{a+b}{3}$\\
(2) $\sqrt{\frac{a^2+b^2+ab}{3}}$\\
(3) $\frac{a+b}{2}$\\
(4) $\sqrt{\frac{a^2+b^2+ab}{2}}$