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

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Fluid Mechanics

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}

)

Answer: 9600

Solution

By Bernoulli's principle applied to the two wing surfaces (same height), the pressure difference across each wing balances the weight:

Δ P = \frac{1}{2} ρ (v_{u pp er}^{2} - v_{l o w er}^{2})

Converting speeds:

180

km/h

= 50

m/s,

252

km/h

= 70

m/s. Total wing area

A = 2 \times 40 = 80 m^{2}

m g = Δ P \times A = \frac{1}{2} (1) (7 0^{2} - 5 0^{2}) (80) = \frac{1}{2} (4900 - 2500) (80) = \frac{1}{2} (2400) (80) = 96000 N

m = \frac{96000}{10} = 9600 kg

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Integer answer

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