The relationship between γ, S, G and e is ______
a) γ=\(\frac{(GS+e) γ_w}{(1+e)}\)
b) γ=\(\frac{(G+eS) γ_w}{(1+e)}\)
c) γ=\(\frac{(G+e)S γ_w}{(1+e)}\)
d) γ=\(\frac{(G+e) γ_w}{(1+e)S}\)

Answer: b
Explanation: The bulk unit weight is given by,
\(γ=\frac{W}{V} = \frac{(γ_s*V_s+ γ_w *V_w)}{V}\)
When V_s = 1, V_w = e_w and V = 1+e
γ = \(\frac{(γ_s*1 + γ_w * e_w)}{(1+e)}\)
since e_w = e*S and γ_s = Gγ_w
γ = \(\frac{(Gγ_w*1 + γ_w * e*S)}{(1+e)}\)
γ=\(\frac{(G+eS) γ_w}{(1+e)}\).