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Q.

The blades of a wndmill sweeps out a circle of area 'A'. If the wind flows at a velocity 'v' perpendicular to the circle (denisity of air = \large \rho )
    A)    the mass of the air passing through it in time 't' is AV\large \rhot
    B)    the kinetic energy of the air is  \large \frac{1}{2}A{v^3}\rho t
    C)    If the windmill converts 25% of the wind energy into electrical energy and \large A = 30{m^2},V = 36kmph,\rho = 1.2kg{m^{ - 3}}  then the electrical power produced is 4.5 kw

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a

A, B, C are false

b

A, B, C are true

c

A false, B & C are true

d

 A, B are true, C is false

answer is D.

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Detailed Solution

Q = rate of volume flow

m = rate of mass flow = ρQ = ρAV

Rate of generation of K.E. = 1/2 mV2 = 1/2 ρAv3.

Total kinetic energy delivered to the air in time t = 1/2 ρ Av3 . t.

Power = η x  1/2 ρ AV3

= 0.25 x 1/2 x 1.2 x 30 x (36 x 5/18)3 W

= 4.5 KW

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