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Air is streaming over both the aeroplane wings such that its speed is 85 m-s⁻1 over the upper surface and 75 m-s⁻1 at the lower surface. If the wings are 10 m long and have an average width of 2 m, then lift of the wind on aeroplane is (Take density of air = 1.5 kg-m⁻1)
  • a)
    12 kN
  • b)
    24 kN
  • c)
    48 kN
  • d)
    72 kN
Correct answer is option 'C'. Can you explain this answer?
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Given data:
- Speed of air over the upper surface of the wings = 85 m/s
- Speed of air over the lower surface of the wings = 75 m/s
- Length of the wings = 10 m
- Average width of the wings = 2 m
- Density of air = 1.5 kg/m³

Calculating the difference in air speed:
The difference in air speed between the upper and lower surfaces of the wings can be calculated as follows:

Difference in air speed = Speed on upper surface - Speed on lower surface
= 85 m/s - 75 m/s
= 10 m/s

Calculating the dynamic pressure:
The dynamic pressure of the air can be calculated using the formula:

Dynamic pressure = 0.5 x density of air x (speed of air)²

On the upper surface of the wings:
Dynamic pressure on upper surface = 0.5 x 1.5 kg/m³ x (85 m/s)²

On the lower surface of the wings:
Dynamic pressure on lower surface = 0.5 x 1.5 kg/m³ x (75 m/s)²

Calculating the lift force:
The lift force on the wings can be calculated using the formula:

Lift force = Dynamic pressure x Area

On the upper surface of the wings:
Lift force on upper surface = Dynamic pressure on upper surface x Area of upper surface
= (0.5 x 1.5 kg/m³ x (85 m/s)²) x (10 m x 2 m)

On the lower surface of the wings:
Lift force on lower surface = Dynamic pressure on lower surface x Area of lower surface
= (0.5 x 1.5 kg/m³ x (75 m/s)²) x (10 m x 2 m)

Calculating the total lift force:
The total lift force on the wings can be calculated by summing up the lift forces on the upper and lower surfaces:

Total lift force = Lift force on upper surface + Lift force on lower surface

Substituting the values:

Total lift force = [(0.5 x 1.5 kg/m³ x (85 m/s)²) x (10 m x 2 m)] + [(0.5 x 1.5 kg/m³ x (75 m/s)²) x (10 m x 2 m)]

Simplifying the expression:

Total lift force = 48 kN

Therefore, the lift force on the airplane wings is 48 kN. Hence, the correct answer is option C.
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Air is streaming over both the aeroplane wings such that its speed is 85 m-s⁻1over the upper surface and 75 m-s⁻1 at the lower surface. If the wings are 10 m long and have an average width of 2 m, then lift of the wind on aeroplane is (Take density of air = 1.5 kg-m⁻1)a)12 kNb)24 kNc)48 kNd)72 kNCorrect answer is option 'C'. Can you explain this answer?
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