Question

The velocity υ of water waves may depend on their wavelength λ density of water ρ and the acceleration due to gravity g. Find relation between these quantities by the method of dimension?

CLASS - XI PHYSICS (Physical World & Measurement)

Answer 1

Let  v = k * λ^a ρ^b g^c
    v = [L] [T]⁻¹   λ = [ L]       ρ = density = [M] [L]⁻³     g = [ L] [T]⁻²

Hence   [L][T]⁻¹ = [M]^b [L]^{a-3b+c} [T]^{-2c}
Comparing the dimensions:
             b = 0.    c = 1/2       => a = 1/2

So   v = k √(gλ)

Answer 2

hoping this may help you......