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`.

Options

A. `upsilon^2 prop lamdag^(-1) rho^(-1)`
B. `upsilon^2 prop glamdarho^(-1)`
C. `upsilon^2 prop glamda`
D. `upsilon^2 prop g^(-1) lamdag^(-3)`

Answer

C

Explanation

`upsilon=lamda^x rho^(y) g^z`
` upsilon=[L]^x [ML^(-3)]^(y)[LT^(-2)]^z`
`[LT^(-1)]=[M^yL^(x-3y+z)T^(-2z)]`
On comparing LHS and RHS,
`y = 0 , x - 3y + z = 1 , -2z =-1`
On solving above equations,
`upsilon prop lamda^(1//2)g^(1//2)implies upsilon^2=lamdag `