A wind powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy, intercepted by its blade into electric energy. For wind speed v, the electrical power output will be proportional to
(Choose one among the four)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
In a unit of time, a unit of mass of wind will pass the blades. The wind has speed v, so the mass' kinetic energy is proportional to v^2. This energy is transfered in part to the blades, and it again proportional to v^2.
Since energy is conserved, and we're told the generator converts a fixed fraction, that fixed fraction of energy is still proportional to v^2.
The answer is v^2.
However, that is not exactly what I asked for. The question asked for the proportionality with the power, NOT Energy.
In my answer, I stated "In a unit of time"...this means an amount of energy proportional to v^2 has been transferred in this unit of time...that's power.