Question

Consider a wire having initial diameter of 2 mm. Poisson’s ratio for material is 0.5. The longitudinal
strain produced in wire is 0.1%. The final diameter of wire is:​

Answer 1

Given:

Initial diameter, D = 2 mm

Poisson's Ratio σ = 0.5

Longitudinal Strain, Δl/l = 0.1 % = 0.1 /100 = 0.001

To Find :

Final Diameter

Calculation:

- Poisson's ratio is given as

σ = Lateral strain / Longitudinal strain

⇒ Lateral Strain = σ × Longitudinal strain

⇒ ΔD / D  = σ × Δl/l

⇒ ΔD = σ × Δl/l × D

⇒ ΔD = 0.5 × 0.001 × 2

⇒ ΔD = 0.001 mm

- Final diameter = Initiat diameter - change in diameter

⇒ D' = D - ΔD

⇒ D' = 2 - 0.001

⇒ D' = 1.999 mm

- So the final diameter will be 1.999 mm