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In a uniform magetic 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 ) $\frac{(B \pi r \omega)^2}{2R}$
( C ) $\frac{(B \pi r^2 \omega)^2}{2R}$
( D ) $\frac{(B \pi r \omega^2)^2}{8R}$

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