A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is______ $\mathrm{kg}$. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
JEE MAIN 2024, Diffcult
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$\mathrm{A}=80 \mathrm{~m}^2$
Using Bernonlli equation
$\mathrm{A}\left(\mathrm{P}_2-\mathrm{P}_1\right)=\frac{1}{2} \rho\left(\mathrm{V}_1^2-\mathrm{V}_2^2\right) \mathrm{A}$
$\mathrm{mg}=\frac{1}{2} \times 1\left(70^2-50^2\right) \times 80$
$\mathrm{mg}=40 \times 2400$
$\mathrm{~m}=9600 \mathrm{~kg}$
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