In a uniform magnetic field of induction $$B$$ a wire in the form of semicircle of radius $$r$$ rotates about the diameter of the circle with angular frequency $$\omega$$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $$R$$ the mean power generated per period of rotation is

A

$$\frac{B\pi r^2 \omega}{2R}$$

B

$$\frac{(B\pi r^2 \omega)^2}{2R}$$

C

$$\frac{(B\pi r \omega)^2}{2R}$$

D

$$\frac{(B\pi r \omega^2)^2}{8R}$$