question_answer

A wind with speed 40 m/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(\[{{\rho }_{air}}=1.2kg/{{m}^{3}}\])

A) \[4.8\times {{10}^{5}}N,upwards\]

B) \[2.4\times {{10}^{5}}N,upwards\]

C) \[2.4\times {{10}^{5}}N,downwards\]

D) \[4.8\times {{10}^{5}}N,downwards\]

Correct Answer: B

Solution :

[b] According to Bernoulli's theorem, \[P+_{2}^{1}\rho {{v}^{2}}={{P}_{0}}+0\] \[So,\,\,\,\Delta P=\frac{1}{2}\rho {{v}^{2}}\] \[F=\Delta PA=\frac{1}{2}\rho {{v}^{2}}A\] \[=\frac{1}{2}\times 1.2\times 40\times 40\times 250=2.4\times {{10}^{5}}N\] (upwards)