A thin rod of length $$l$$ in the shape of a semicircle is pivoted at one of its ends such that it is free to oscillate in its own plane. The frequency $$f$$ of small oscillations of the semicircular rod is

A

$$\frac{1}{2\pi}\sqrt{\frac{g\pi}{2l}}$$

B

$$\frac{1}{2\pi}\sqrt{\frac{g\sqrt{\pi^2 + 4}}{2l}}$$

C

$$\frac{1}{2\pi}\sqrt{\frac{g(\pi + 2)}{l}}$$

D

$$\frac{1}{2\pi}\sqrt{\frac{g(\pi^2 + 1)}{2\pi l}}$$