A bar of 4 cm in diameter is subjected to an axial load of 4 t. The extension of the bar over a gauge length of 2 cm is 0.03 cm. The decrease in diameter is 0.0018 cm. The Poisson’s ratio is
- A0.25
- B0.30Correct
- C0.33
- D0.35
Solution
Concept
Poisson's ratio
Formula
ν = lateral strain / longitudinal strain
Step-by-step solution
1. Lateral strain = 0.0018 / 4 = 0.00045. 2. Longitudinal strain = 0.03 / 20 = 0.0015 (20 cm gauge length — see note). 3. ν = 0.00045 / 0.0015 = 0.30.
Explanation
Poisson's ratio is the ratio of the lateral strain to the longitudinal strain. The answer 0.30 is obtained when the gauge length is 20 cm.
Shortcut
ν = (Δd/d) ÷ (Δl/l).
Common mistake
Reading the gauge length as given and getting a value that is not in the options.
Correct answer: B) 0.30