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JEE Main 2013 (25 Apr, Shift 1) · Power

Power question from JEE Main 2013 (25 Apr, Shift 1)

Q39JEE Main 2013 · 25 APR · SHIFT 1Easy

Power

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 $v$ , the electrical power output will be most likely proportional to

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Answer: (d)

Mass of air hitting blades per second $= \rho A v$ .
KE carried per second $= \dfrac{1}{2}(\rho A v)v^2 = \dfrac{1}{2}\rho A v^3$ .
Output is a fixed fraction of this, so $P \propto v^3$ .
So the answer is (d) $v^3$ .

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