A plane is in level flight at constant speed and each of its two wings has an area of 40 m 2 . If the speed of the air is 180 km / h over the lower wing surface and 252 km / h over the upper wing surface, the mass of the plane is \ \ \ \ \ \ \ kg. (Take air density to be 1 kg m -3 and g =10 ms -2 )

Physics · Fluid Mechanics

JEE Main 2024 — 1 February, Shift 1 — Question 54

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 $\_\_\_\_\_\_\_$ kg. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

Answer: 9600

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{A}=80 \mathrm{~m}^{2}$ 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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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Physics
Chapter: Fluid Mechanics
Topic: Bernoulli's Equation and its Applications

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