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