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Q.

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts afixed fraction of the wind energy intercepted by its blades into electric  energy. For wind speed v, the electric power output will be proportional to

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a

v

b

v2

c

v3

d

v4

answer is C.

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Detailed Solution

The force F exerted by the wind on the blades of the generator is given byF=ρAv2  where, ρ= density of air  A= area of cross-section of blade  V= velocity of wind  ∴  Power output, P=∫Fdv =∫ρAv2dv=ρAv3/3 ρ∝v3
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