The speed of ripples ( v ) on water surface depends on surface tension ( σ ) , density ( ρ ) , and wavelength ( λ ) . Then the square of speed ( v ) is proportional to

Step-by-step solution

Speed of ripples, v depends on σ , ρ , λ ⇒ v ∝ σ a ρ b λ c ⇒ M 0 L T - 1 ∝ M T - 2 a M L - 3 b L c ⇒ M 0 L T - 1 ∝ M a + b L - 3 b + c T - 2 a By equating the powers, ⇒ a + b = 0 ,   - 3 b + c = 1 ,   - 2 a = - 1 ⇒ a = 1 2 ,   b = - 1 2 ,   c = - 1 2 ⇒ v ∝ σ 1 2 ρ - 1 2 λ - 1 2 ⇒ v ∝ σ ρ λ ⇒ v 2 ∝ σ ρ λ