# The volume of a soil sampler is 45 cm3. When the soil collected by it is poured into a graduated jar, the volume of water displaced by it is 20 cm3. T

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The volume of a soil sampler is 45 cm3. When the soil collected by it is poured into a graduated jar, the volume of water displaced by it is 20 cm3. The void ratio and porosity of the soil will be
1. 0.555 and 1.25
2. 1.25 and 0.555
3. 0.692 and 2.25
4. 2.25 and 0.692

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Correct Answer - Option 2 : 1.25 and 0.555

Concept:

Void ratio (e):

Void ratio is usually defined as the ratio of the volume of voids to the total volume of soil solid.

Porosity (n):

Porosity is defined as the ratio of the volume of voids to the total volume of the soil.

The relationship between void ratio and porosity are as follows:

$\rm{e=\frac{n}{1-n}\; and\; n=\frac{e}{1+e}}$

Calculation:

Given, V = 45 cm3

Volume of water displaced = volume of solids

VS = 20 cm3

Volume of voids, VV = V – VS = 45 – 20 = 25 cm3

$\therefore {\rm{e}} = {\rm{\;}}\frac{{{{\rm{v}}_{\rm{v}}}}}{{{{\rm{V}}_{\rm{s}}}}} = {\rm{\;\;}}\frac{{25}}{{20}} = 1.25$

Relationship between Void ratio and Porosity:

$n=\frac{e}{1+e}$

$n=\frac{1.25}{1+1.25}$ = 0.555