The soil has a liquid limit of 50%. Following the A-line, in the plasticity chart as per IS : 1498-1970, the corresponding plastic limit is:
- A28.1%Correct
- B25%
- C21.9%
- DInsufficient data
Solution
Concept
On the A-line, the plasticity index is PI = 0.73(LL − 20). The plastic limit is then PL = LL − PI.
Formula
PI = 0.73(wL − 20); wP = wL − PI
Step-by-step solution
1. A-line equation: PI = 0.73(wL − 20) 2. wL = 50%, so PI = 0.73 × (50 − 20) = 0.73 × 30 = 21.9% 3. Plastic limit wP = wL − PI = 50 − 21.9 = 28.1%
Explanation
A soil that lies on the A-line has PI = 0.73(LL − 20). For LL = 50%, PI = 21.9%. Plastic limit = LL − PI = 28.1%.
Why the other options are wrong
B: 25% does not come from the A-line equation. C: 21.9% is the plasticity index, not the plastic limit. D: The data is enough because the A-line equation gives PI.
Shortcut
PL = LL − 0.73(LL − 20) = 0.27 LL + 14.6 = 13.5 + 14.6 = 28.1%
Common mistake
Giving the PI value (21.9%) as the plastic limit.
Correct answer: A) 28.1%