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.


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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