A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $u$ , the electrical power output will be proportional to

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$u$

$u^{2}$

$u^{3}$

$u^{4}$

answer is C.

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Detailed Solution

$F = u (\frac{d m}{d t}) = u \frac{d}{d t} ρ \times v o l u m e = u ρ \frac{d}{d t} v o l u m e - u ρ A u = A ρ u^{2}$ $P o w e r = F o r c e \times V e l o c i t y = A ρ u^{2} \times u = A ρ u^{3}$

$P \propto u^{3}$

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