The speed `(v)` of ripples on the surface of waterdepends on surface tension `(sigma)`, density `(rho)` 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

`v prop sigma^(x)rho^(y)lambda^(z)`
`v=ksigma^(x)rho^(y)lambda^(z)`
`[LT^(-1)]=[MT^(-2)]^(x)[ML^(-3)]^(y)[L]^(z)`
`x+y=0" "," "-2x=-1" "," "-3y+z=1`
`x=1/2" "y=-1/2" "z=-1/2`
Hence, `v=(sigma^(1//2))/(rho^(1//2)lambda^(1//2))`
`v^(2) equiv (sigma/(rho lambda))`