### Neet Solved Paper 2015 Question 18

##### Question: A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is . 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}=1.2kg/m^{3}) $

#### Options:

A) $ 4.8\times 10^{5}N $ N, downwards

B) $ 4.8\times 10^{5}N $ , upwards

C) $ 2.4\times 10^{5}N $ , upwards

D) $ 2.4\times 10^{5}N $ , downwards

## Show Answer

#### Answer:

Correct Answer: C

#### Solution:

From Bernoulli’s theorem $ p _1+\frac{1}{2}\rho v_1^{2}=p _2+\frac{1}{2}\rho v_2^{2} $

where, $ p _1,p _2 $ are pressure inside and outside the roof and

$ v _1,v _2 $ are velocities of wind inside and outside the roof. Neglect the width of the roof.

Pressure difference is $ p _1-p _2=\frac{1}{2}\rho (v_2^{2}-v_1^{2}) $ $ =\frac{1}{2}\times 1.2(40^{2}-0)=960N/m^{2} $

Force acting on the roof is given by $ F=(p _1+p _2)A=960\times 250 $ $ =24\times 10^{6}N=24\times 10^{5}N $

As the pressure inside the roof is more than outside to it.

So the force will act in the upward direction. i.e. $ F=2.4\times 10^{5}N $ upward.