The speed v of a water wave is assumed to depend on wavelength λ, gravitational acceleration g and water density ρ as v = λᵃgᵇρᶜ. The values of a, b and c are:
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Question

The speed v of a water wave is assumed to depend on wavelength λ, gravitational acceleration g and water density ρ as v = λᵃgᵇρᶜ. The values of a, b and c are:

G1 Physics · Accepted Answer

Assume: v = λᵃgᵇρᶜ Dimensions: [LT⁻¹] = [L]ᵃ[LT⁻²]ᵇ[ML⁻³]ᶜ = Mᶜ Lᵃ⁺ᵇ⁻³ᶜ T⁻²ᵇ Comparing powers: Mass: c = 0 Time: -2b = -1 ⇒ b = 1/2 Length: a + b = 1 ⇒ a = 1/2 Therefore: a = 1/2, b = 1/2, c = 0 Hence option C.