Experiments reveal that the velocity `v` of water waves may depend on their wavelength `lambda`, density of water `rho`, and acceleration due to gravity `g`. Establish a possible relation between `v and lambda , g, rho`.

Explanation

Let `upsilon = K. lambda^a rho^b g^c,` where K is
dimensionles constant of proportionality.
`[M^0L^1T^(-1)] = L^a (ML^(-3))^b(LT^(-2))^c`
` = M^b L^(a - 3b +c) T^(-2c)`
Applying principle of homogeneity of
dimensions, we get
`b = 0, a - 3b + c =1 , -2c = 1, c = (1)/(2)`
`:. a - 0 +(1)/(2) =1, a =1 -(1)/(2) =(1)/(2)`
Hence `upsilon = K sqrt(lambda g)`