$\text { At time t Flux of the magnetic field is }$

$\phi = B A cos\omega t = \frac{1}{2} B \pi r^2 cos\omega t$

$\Rightarrow \text{Induced emf}\xi = -\frac{d\phi}{dt} =\frac{1}{2} B \pi r^2\omega  sin\omega t$

$\text{Power } P = \frac{\xi^2}{R} = \frac{B^2 \pi^2 r^4 \omega^2 sin^2\omega t}{4R} $

$\text{Average Power } P_{av} = \frac{B^2 \pi^2 r^4 \omega^2}{8R} $