A plane is in level flight at constant speed and each of its two wings has an area of 25 m². If the speed of the air on the upper and lower surfaces of the wing are 270 km / h and 234 km/h respectively, then what must have been the mass of the plane? (Take the density of the air = $1 \mathrm{kg} {\mathrm{m}}^{-3}$) 

Let $v_1,v_2$ are the speed of air on the lower and upper surface S of the wings of the plane P1 and P2 are the pressure there,
According to Bernoulli's theorem

${\mathrm{P}}_1+\frac{1}{2}\rho {\mathrm{v}}_1^2={\mathrm{P}}_2+\frac{1}{2}\rho {\mathrm{v}}_2^2$

${\mathrm{P}}_1-{\mathrm{P}}_2=\frac{1}{2}\left(\rho {\mathrm{v}}_2^2-{\mathrm{v}}_1^2\right)$

$\text{ Here, }{v}_1=234{\mathrm{kmh}}^{-1}=234\times \frac{5}{18}{\mathrm{ms}}^{-1}$

$=65{\mathrm{ms}}^{-1}$

$v_2=270{\mathrm{kmh}}^{-1}=270\times \frac{5}{18}$

$=75{\mathrm{ms}}^{-1}$

$\text{ Area of wings }=2\times 25{\mathrm{m}}^2=50{\mathrm{m}}^2$

$\therefore {\mathrm{P}}_1-{\mathrm{P}}_2=\frac{1}{2}\times \left({75}^2-{65}^2\right)$

Upward force on the plane

$=\left({\mathrm{P}}_1-{\mathrm{P}}_2\right)\mathrm{A}$

$=\frac{1}{2}\times 1\times \left({75}^2-{65}^2\right)\times 50\mathrm{m}$

As the plane is in level flight, therefor upward force balances the weight of the plane.

$\therefore \mathrm{mg}=\left({\mathrm{P}}_1-{\mathrm{P}}_2\right)\mathrm{A}$

Mass of the plane,

$\mathrm{m}=\frac{\left({\mathrm{P}}_1-{\mathrm{P}}_2\right)}{\mathrm{g}}\mathrm{A}=\frac{1}{2}\times \frac{1\times \left({75}^2-{65}^2\right)}{10}\times 50$

$=\frac{(75+65)(75-65)\times 50}{2\times 10}=3500 \mathrm{kg}$