# The mass of a chunk of moist soil is 20 kg and its dry density is 1500 kg/m3. What is the void ratio of the soil if the specific gravity is 2.50 and t

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The mass of a chunk of moist soil is 20 kg and its dry density is 1500 kg/m3. What is the void ratio of the soil if the specific gravity is 2.50 and the density of water is 1000 kg/m3?
1. 44.45%
2. 72.35%
3. 66.67%
4. 56.67%

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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.

$\gamma_d$ = W/ 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%