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