A) \[\frac{1}{2}\rho A({{v}_{1}}-{{v}_{2}})\]
B) \[\frac{1}{2}\rho A({{v}_{1}}+{{v}_{2}})\]
C) \[\frac{1}{2}\rho A(v_{1}^{2}-v_{2}^{2})\]
D) \[\frac{1}{2}\rho A(v_{1}^{2}+v_{2}^{2})\]
Correct Answer: C
Solution :
Due to specific shape of wings when the aeroplane runs, air passes at hrgher speed over it as compared to its lower surface. This difference of air speeds above and below the wings in accordance with Bernoullis principle, creates a pressure difference, due to which an upward force called dynamic lift acts on the plate. \[\therefore \]Upward lift = Pressure difference x area of wing\[=\frac{1}{2}\rho A(v_{1}^{2}-v_{2}^{2})\]
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