If 90% of soil particles got retained over 2 mm sieve and 50% of soil particles got retained over 4.75 mm sieve, then the effective diameter of the soil will be:
- A2 mmCorrect
- B4.75 mm
- C1.25 mm
- D6.75 mm
Solution
Concept
Effective diameter (D10) is the particle size at which 10% of the soil (by weight) is finer.
Formula
% finer = 100 − % retained; D10 = size at 10% finer
Step-by-step solution
1. 90% is retained on the 2 mm sieve. 2. So % finer than 2 mm = 100 − 90 = 10%. 3. Effective size D10 is the size at which 10% is finer. 4. So D10 = 2 mm.
Explanation
Effective diameter means D10, the size for which 10% of the soil is finer. Since 90% is retained on the 2 mm sieve, only 10% passes it. So D10 = 2 mm.
Why the other options are wrong
B: 50% is retained on 4.75 mm, so 50% is finer; 4.75 mm is D50, not D10. C: 1.25 mm is not given by any data in the question. D: 6.75 mm is just 2 + 4.75 added, which has no meaning.
Shortcut
10% passing = 90% retained, so the sieve with 90% retained gives D10 directly.
Common mistake
Taking % retained as % finer, or picking the 50% value (D50) as the effective size.
Correct answer: A) 2 mm