A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will beρair =1.2 kg/m3
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a
2.4×105 N, upwards
b
2.4×105 N, downwards
c
4.8×105 N, downwards
d
4.8×105 N, upwards
answer is A.
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Detailed Solution
By Bernoulli's theorem, P1+12ρv12⏟inside =P2+12ρv22⏟outside Assuming that the roof width is very small Pressure difference,P1-P2=12ρv22-v12 Here, ρ=1.2 kg m-3,v2=40 m s-1,v1=0A=250 m2P1-P2=12×1.2402-02=12×1.2×1600=960 N m-2 Force acting on the roof F=P1-P2×A=960×250=2.4×105 N upwards