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 $$\frac{\sigma_0}{r}$$, then the radius of gyration of the disc about its axis passing through the center is

A

$$\frac{a+b}{3}$$

B

$$\sqrt{\frac{a^2 + b^2 + ab}{3}}$$

C

$$\frac{a+b}{2}$$

D

$$\sqrt{\frac{a^2 + b^2 + ab}{2}}$$