Question

A steel wire having cross-sectional area 2 mm² is stretched by 10 N. Find the lateral strain produced in the wire.

(Given: Y for steel = 2 × 10¹¹ N/m², Poisson’s ratio σ = 0.29)

Answer 1

Given: A = 2 mm² = 2 × 10^-6 m²,

F = 10 N, Y_steel = 2 × 10¹¹ N/m², σ = 0.29

To find: Lateral strain

Formulae:

i. Longitudinal stress = \(\frac{F}{A}\)

Calculation: From formula (i),

longitudinal stress = \(\frac{10}{2\times10^{-6}}\)

= 5 × 10⁶ N/m²

From formula (ii),

From formula (iii),

lateral strain = σ × longitudinal strain

= 0.29 × 2.5 × 10^-5

∴ lateral strain = 7.25 × 10^-6

Lateral strain produced in the wire is 7.25 × 10^-6.