Question

The velocity of water waves (v) may depend on 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 is
(a) v
(b) v² $\ \propto$ gλ
(c) v² $\ \propto$ gλ²
(d) v² $\ \propto$ g⁻¹λ²

Answer 1

option b is correct :v^2g

Answer 2

Answer:

Explanation:

Velocity of water waves = v

Wavelength = λ

Density of water = p

Acceleration due to gravity = g

Thus,

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

v = k √(gλ)