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### Mechanical Properties of Fluids NCERT Solutions Class 11 Physics - Solved Exercise Question 10.27

Question 10.27:
A plane is in level flight at constant speed and each of its two 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 m–3).
Solution:
The area of the wings of the plane, A = 2 × 25 = 50 m2
Speed of air over the lower wing, V1 = 180 km/h = 50 m/s
Speed of air over the upper wing, V2 = 234 km/h = 65 m/s
Density of air, ρ = 1 kg m–3
Pressure of air over the lower wing = P1
Pressure of air over the upper wing= P2
The upward force on the plane can be obtained using Bernoulli’s equation as:
P1 + (1/2) ρ V12  =  P2 + (1/2) ρ V22
P1 - P2 = (1/2) ρ ( V22 - V12)   .....(i)
The upward force (F) on the plane can be calculated as:
(P1 - P2)A  =  (1/2) ρ ( V22 - V12) A
= (1/2) X 1 X (652 - 502) X 50
= 43125 N
Using Newton’s force equation, we can obtain the mass (m) of the plane as:
F = mg
∴ m = 43125 / 9.8 = 4400.51 kg
∼ 4400 kg
Hence, the mass of the plane is about 4400 kg.