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Properties of Matter question

2024 · 29 Jan · Shift 1 · Q90
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Properties of Matter question

2024 · 29 Jan · Shift 1 · Q90

JEE MainPhysicsProperties of MatterNumerical+4 / −1
In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are 70 ms−170 \mathrm{~ms}^{-1}70 ms−1 and 65 ms−165 \mathrm{~ms}^{-1}65 ms−1 respectively. If the wing area is 2 m22 \mathrm{~m}^22 m2, the lift of the wing is ‾N\underline{\hspace{2cm}}N​N. (Given density of air =1.2 kg m−3=1.2 \mathrm{~kg} \mathrm{~m}^{-3}=1.2 kg m−3)
Numerical answer
View written solutionFree

Correct answer: 810

  1. Use Bernoulli’s principle

For airflow over the upper and lower surfaces of the wing at the same height,

P+12ρv2=constantP + \frac{1}{2}\rho v^2 = \text{constant}P+21​ρv2=constant

Hence, the pressure difference between lower and upper surfaces is

Plower−Pupper=12ρ(vupper2−vlower2)P_{\text{lower}} - P_{\text{upper}} = \frac{1}{2}\rho\left(v_{\text{upper}}^2 - v_{\text{lower}}^2\right)Plower​−Pupper​=21​ρ(vupper2​−vlower2​)

Given:

vupper=70 m s−1,vlower=65 m s−1,ρ=1.2 kg m−3v_{\text{upper}} = 70\ \text{m s}^{-1}, \quad v_{\text{lower}} = 65\ \text{m s}^{-1}, \quad \rho = 1.2\ \text{kg m}^{-3}vupper​=70 m s−1,vlower​=65 m s−1,ρ=1.2 kg m−3

So,

ΔP=12(1.2)(702−652)\Delta P = \frac{1}{2}(1.2)\left(70^2 - 65^2\right)ΔP=21​(1.2)(702−652)

  1. Calculate the speed-square difference

702=4900,652=422570^2 = 4900, \qquad 65^2 = 4225702=4900,652=4225

4900−4225=6754900 - 4225 = 6754900−4225=675

Thus,

ΔP=0.6×675=405 Pa\Delta P = 0.6 \times 675 = 405\ \text{Pa}ΔP=0.6×675=405 Pa

  1. Compute lift force

Lift is pressure difference multiplied by wing area:

F=ΔP⋅AF = \Delta P \cdot AF=ΔP⋅A

Given wing area,

A=2 m2A = 2\ \text{m}^2A=2 m2

Therefore,

F=405×2=810 NF = 405 \times 2 = 810\ \text{N}F=405×2=810 N

  1. Final answer

810 N\boxed{810\ \text{N}}810 N​

This matches the stored correct answer.

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