The speed `(v)` of ripples on the surface of waterdepends on surface tension `(sigma)`, density `(phi)` and wavelength `(lambda)`. The square of speed `(v)` is proportional to

Options

A. `(sigma)/(rho lambda)`
B. `(rho)/(sigma lambda)`
C. `(lambda)/(sigma rho)`
D. `rho lambda sigma`

Answer

a

Explanation

Let `v prop sigma^(a)rho^(b)gamma^(c )`
Equatiing dimension on both sides,
`[M^(0)L^(1)T^(1)]prop[M^(T-2)]^(a)[ML^(-3)]^(b)[L]^(c ) prop [M]^(a+b)[L]^(-3b+c)[T]^(-2a)`
Equating the powers of M,L,T on both sides, we get
`a+b=0`
`-3b+c=1`
`-2a= -1`
Solving, we get
`a=1/2,b= -1/2,c= -1/2`
`:. v prop sigma^(1//2)rho^(-1//2)lambda^(-1//2)`
`:. v^(2) prop (sigma)/(rho lambda)`