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Question

A plane is in a level flight at a constant speed and each of its two wings has an area of 50 m2. If the speed of air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the plane's mass is [Lift force on the wings = weight of plane]
(Take density of air = 1 kg/m3 and g=10 m/s2)
  1. 2.4×104 kg
  2. 4.4×104 kg
  3. 1.2×104 kg
  4. 3.6×104 kg


Solution

The correct option is C 1.2×104 kg
Applying the Bernoulli's theorem above and below the wings, we get 
P1+12ρV21+ρgh1=P2+12ρV22+ρgh2
[h1=h2]
P1P2=12ρ[V22V21].....(1)
Given, v1=180 km/h=50 m/s and 
 v2=252 km/h=70 m/s
ρ=1 kg/m3
P1P2=12(702502)
P1P2=1200 Pa.....(2)
Area of both wings =2×50=100 m2

Now, 
Upward force on the plane =(P1P2)A=1200×100=1.2×105 N

As the plane is in level flight, therefore upward force balances the weight of the plane.
mg=1.2×105 N

So, mass of the plane =1.2×104 kg

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