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A wind with speed 40m /s blows parallel ...

A wind with speed 40m /s blows parallel to the roof of a house. The area of the roof is 250`m^2`. 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 be `[p_("air")=1.2 kg//m^3]`

A

`4.8xx10^5 N`, downwards

B

`4.8xx10^5 N,` upwards

C

`2.4 xx 10^5 N, `upwards

D

`2.4 xx 10^5 N,` downwards

Text Solution

Verified by Experts

The correct Answer is:
C
According to Bernoulli.s theorem,
`p+1/2rho v^2=` constant
When pressure inside that house = atmospheric pressure , `p_0`.
Let the pressure on the roof be P.
`therefore p+1/2 rho v^2 = p_0+`
Clearly, `p_0 gt p`
So, effective pressure `p_0-p` will act in the upward direction .
`p_0-p=1/2 rho v^2=1/2xx1.2xx(40)^2`
Hence, effective force
`=1/2xx1.2xx(40)^2xx250=2.4x10^5 N`
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