Given, speed of ripple of water =v Surface tension =σ Density =ρ Wavelength =λ As we know that, σ=
Force
Length
and dimensional formula of σ=
[MLT−2]
[L]
=[ML0T−2] and dimensional formula of ρ,v and λ are [ML−3T0],[M0LT−1] and [M0LT0]. Let [σ]=[ρ]a[v]b[λ]c ⇒[ML0T−2]=[ML−3T0]a[M0LT−1]b[M0LT0]c =[MaL−3a+b+cT−b] ⇒a=1 ⇒b=2 ⇒−3a+b+c=0 ⇒−3+2+c=0 c = 1 ∴[σ]=[ρ]1[v]2[λ]1 Hence, σ∝ρv2λ ⇒v2∝