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/(rholamda)`
B. `rho/(sigmalamda)`
C. `lamda/(sigmarho)`
D. `rho lamdasigma`

Answer

A

Explanation

`vpropsigma^(x) rho^(y) lamda^(z) : sigma rarr ` Surface tension , `rho rarr` density
`[LT^(-1)]=[MT^(-2)] xx[ML^(-3)]^(gamma)[L]^z`
`=[M^(x+y )L^(-3y+z)T^(-2x)]`
`x+ y = 0`
`-3y + z = 1`
`-2x = -1`
On solving the equations we get 
`x=1/2 , y =1/2 ,z=1/2`