Question

1. The force, F, acting on the wings of an aircraft moving through air of velocity, v, and density, ρ, is given by the equation F=kvᵖρᵠAᶻ, where k is a dimensionless constant and A is the surface area of the wings. Use dimensional analysis to determine the values of x, y and z.

Accepted Answer

By dimensional analysis: F=[MLT⁻²], v=[LT⁻¹], ρ=[ML⁻³], A=[L²]. Equating: MLT⁻²=(LT⁻¹)ˣ(ML⁻³)ʸ(L²)ᶻ. Comparing powers: for M: y=1; for T: -x=-2 → x=2; for L: x-3y+2z=1 → 2-3+2z=1 → 2z=2 → z=1. Thus x=2, y=1, z=1.

WAEC Physics 2023 Theory — Question 1

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