JEE Mains · Physics · STD 11 - Fluid mechanics
- JEE Mains 2024
- Hard
- Numerical
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 \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(9600\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A}=80 \mathrm{~m}^2\)
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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