Index Properties MCQ with answer and solution

Concept

Relationship between soil porosity and void ratio

Formula

e = n / (1 - n)

Step-by-step solution

1. Given porosity n = 50% = 0.5. 2. The relation between void ratio (e) and porosity (n) is given by e = n / (1 - n). 3. Substituting n = 0.5: e = 0.5 / (1 - 0.5) = 0.5 / 0.5 = 1. Answer: C

Explanation

Void ratio is related to soil porosity by the formula where void ratio equals porosity divided by one minus porosity. Substituting a porosity of 0.50 into this relationship yields a void ratio of 0.50 divided by 0.50, which equals 1. Thus, when porosity is 50 percent, the volume of voids equal the volume of solid particles, resulting in a void ratio of 1.

Why the other options are wrong

A) A void ratio of 0 is impossible because soil always contains void spaces. B) 0.5 represents the porosity value (50%) rather than the void ratio. D) A void ratio of 1.5 corresponds to a higher porosity of 60%.

Shortcut

Void ratio e = n / (1 - n); for 50% porosity (0.5), e = 0.5 / 0.5 = 1.

Common mistake

Selecting 0.5 by confusing porosity directly with void ratio instead of applying the formula e = n / (1 - n).