Correct Answer - Option 3 : 66.67%
Concept:
Dry Unit Weight(\(\gamma_d\)):
It is a measure of the weight of solid particles per unit volume.
\(\gamma_d\) = Ws / V
Where Ws = weight of solid particles, V = Volume of solid particles
Now the relationship between the specific gravity of solid particles, void ratio, and dry unit weight
\(\gamma_d = {G\gamma_w \over (1+e)}\)
where G = specific gravity of solid particles, e = void ratio
Calculation:
Given Data:
The mass of a chunk of moist soil = 20 kg
The dry density of soil(\(\gamma_d\)) = 1500 kg/m3
Specific gravity(G) = 2.50
The density of water(\(\gamma_w\)) = 1000 kg/m3
Using the relationship between the specific gravity of solid particles, void ratio, and dry unit weight
\(\gamma_d = {G\gamma_w \over (1+e)} \)
\(1500 = {2.50\times 1000 \over (1+e)} \)
\((1+e) = {2.50\times 1000 \over 1500} \)
e = 0.6667
The void ratio is 66.67%