Question

the velocity of matter waves may depend upon their wavelength the density of water and acceleration due to gravity the method of dimensional analysis gives the relation between these quantities as

Answer 1

Let  v = k * λ^a ρ^b   v = [L] [T]⁻¹   (λ)wave length = [ L] ρ = density of water = [M] [L]⁻³     gravity (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

HEY mate here is your answer.

hope it helps you.