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The velocity of water waves v may depend upon their wavelength λ , the density of water ρ and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

Options

  1. Av 2 ∝ ρ g
  2. Bv 2 ∝ g λ ρ
  3. Cv 2 ∝ g λ
  4. Dv 2 ∝ g − 1 λ − 3

Correct answer

C. v 2 ∝ g λ

Step-by-step solution

Let v x = k g y λ z ρ δ . Now by substituting the dimensions of each quantities and equating the powers of M , L and T we get δ = 0 and x = 2 , y = 1 , z = 1 .

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