Ncert Exercises & Solutions

10.27 A plane is in level flight at a 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).

The area of two wings of the plane, A = 2 × 25 = 50 m²

Speed of air over the lower wing surface, v₁ = 180 km/h = 50 m/s

Speed of air over the upper wing surface, v₂ = 234 km/h = 65 m/s

The density of air, ρ = 1 kg m^–3

Using Bernoulli’s equation:

$P_{1} + \frac{1}{2} {ρV}_{1}^{2} = P_{2} + \frac{1}{2} {ρV}_{2}^{2}$
$P_{1} - P_{2} = \frac{1}{2} ρ (V_{2}^{2} - V_{1}^{2}) . . . (i)$

$The upward force (F) on the plane = (P_{1} - P_{2}) A = \frac{1}{2} ρ (V_{2}^{2} - V_{1}^{2}) A = \frac{1}{2} \times 1 \times ({(65)}^{2} - {(50)}^{2}) \times 50 = 43125 N$

Using Newton’s force equation,

$Force of on the plane, F = mg Mass of the plane, m = \frac{43125}{9.8} = 4400.51 kg ~ 4400 kg$

Hence, the mass of the plane is about 4400 kg.

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