The velocity of the waves on the surface of water is proportional to - g y where - wave length- - - density and g - acceleration due to gravity- Which of the following relation is correct -

In each of $α$ $β$ and $γ$ $is a positive acute angle such that$
$sin (α + β - γ) = \frac{1}{2}, cos (β + γ - α) = \frac{1}{2} and tan (γ + α - β) = 1$
Find the values of $α$ , $β$ , & $γ$ .

Q. If

α

β

γ

are the roots of

x^{3} + a x^{2} + b = 0

, then the value of determinant

Δ

is , where

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α & β & γ β & γ & α γ & α & β \end{matrix} ∣ ∣ ∣ ∣ ∣

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The velocity of the waves on the surface of water is proportional to λαρβgy where λ= wave length, ρ= density and g = acceleration due to gravity. Which of the following relation is correct ?

The correct option is B γ=α≠βDimensions of:Velocity of waves =[LT−1]Wavelength =[L]Density =[ML−3]g=[LT−2]v=[λαρβgγ][(LT−1)]=[(L)α(ML−3)β(LT−2)γ][LT−1]=[Lα−3β+γMβT−2γ]on equating the powers we get,β=0,γ=12,α=12Hence, α=γ≠β

The velocity of the waves on the surface of water is proportional to $λ^{α} ρ^{β} g^{y}$ where $λ =$ wave length, $ρ =$ density and g $=$ acceleration due to gravity. Which of the following relation is correct ?