A copper wire of cross-sectional area 0.01 cm2 is under a tension of 20 N. Find the decrease in the cross-sectional area. Young's modulus of copper = 1.1 x 1011 N/m2 and Poisson's ratio = 0.32.
Cross-sectional area A =0.01 cm²
→A = 0.01/10000 =1x10⁻⁶ m²
Stress = 20/1x10⁻⁶ N/m² =2x10⁷ N/m²
Hence the longitudinal strain =Stress/Y =2x10⁷/1.1x10¹¹ =1.82x10⁻⁴
Poisson's ratio = 0.32
Lateral strain = 0.32*1.82x10⁻⁴ =5.82x10⁻⁵
Taking the cross-section as circular with diameter D.
(ΔD/D)/(ΔL/L) =σ
so, ΔD/D = Lateral strain = 5.82x10⁻⁵
We have area A = πD²/4
dA =2πD.dD/4
Hence dA/A =2.dD/D
→dA =2A(dD/D)
→dA =2*0.01*(5.82x10⁻⁵) cm²
=1.164x10⁻⁶ cm²