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 = 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)[ML^(-3)]^(beta)[LT^(-2)]^(gamma)`
`[LT^(-1)]=[L^(alpha-3beta+gamma)M^(beta)T^(-2gamma)]`
Comparing,
`beta=0, gamma=1/2, alpha-3 beta+gamma=1`
`alpha-0+1/2=1`
`alpha=1/2`
`:. gamma = alpha ne beta`