Answer: %(∆W) = 0.37%
Step-by-step explanation:
According to Newton's law of gravitation which states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
F = Gm1m2/r^2
Where
F = force between the masses
G universal gravitational constant
m1 and m2 = mass of the two particles
r = distance between the centre of the two mass
Therefore, weigh of an object on earth is inversely proportional to the square of its distance from the centre of the earth
W₁/W₂ = r₂²/r₁² .....1
W₂ = W₁r₁²/r₂²
At sea level the weight of the plane is W1 and at distance r₁ from the centre of the earth which is equal to the radius of the earth.
The radius of the earth is = 6378.1km
r₁ = radius of the earth = 6 378.1km = 6,378,100m
r₂ = r₁ + 11,719.342m = 6,378,100m + 11,719.342m
r₂ = 6,389,819.342m
W₂ = W₁r₁²/r₂²
W₂ = W₁[(6378100)²/(6,389,819.342)²]
W₂ = W₁[0.996335234422]
W₂/W₁ = 0.9963
fraction reduction of the weight is
ΔW/W₁ = 1 - W₂/W₁ = 1 - 0.9963 = 0.0037
percentage change :
%(∆W) = 0.0037 × 100% = 0.37%
Therefore, the percentage weight loss is 0.37%