The velocity of the waves on the surface of water is proptional to `lambda^(a) rho^(beta) g^(gamma)` where `lambda` = waver length, `rho` = density and `g` =m acceleration due to gravity. Which of the following relation is correct?

Options

A. `alpha = beta ne gamma`
B. `beta = gamma ne alpha`
C. `gamma = alpha ne beta`
D. `alpha ne beta ne gamma`

Answer

C

Explanation

`v prop lambda^(alpha) rho^(beta) g^(gamma) , LT^(-1) = L^(alpha) M^(beta) L^(-3 beta) L^(gamma) T^(-2 gamma)`
Comparing the powers on both sides, we get `alpha,beta` and `gamma`