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Home » A plane is in level flight at constant speed and each of its wings has an area of 25 m2. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg/m3), g = 9.8 m/s2
A plane is in level flight at constant speed and each of its wings has an area of 25 m2. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg/m3), g = 9.8 m/s2
CBSE | Class 11 | Mechanical Properties of Fluids | NCERT | Physics
A plane is in level flight at constant speed and each of its wings has an area of 25 m2. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg/m3), g = 9.8 m/s2

Answer :

Area of the wings of the plane, A=2×25=50 m2
Speed of air over the lower wing, V1
​=180km/h= 180 x (5/18) = 50 m/s

Speed of air over the upper wing, V2
=234km/h= 234 x (5/18) = 65 m/s

Density of air, =1kg/m3
Pressure of air over the lower wing =P1
​Pressure of air over the upper wing =P2
​Pressure difference,ΔP = P1​−P2 = (1/2) ρ (V22 – V12)

= (1/2) x 1 x (652 – 502) = 862.5 Pa

​The net upward force F=ΔP x A
The upward forces balances the weight of the plane

mg = ΔP x A

m = (ΔP x A)/g

= (862.5 x 50)/9.8​
=4400kg

The mass of the plane is 4400kg

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