The ratio of lateral contractional strain and the longitudinal elongational strain of a stretched wire is

The volume of the wire before stretching and after stretching remains the same. HenceπR2L=π(R−ΔR)2(L+ΔL)where ∆L = elongation in wire, and∆R = contraction in radius after stretchingNow L+ΔLL=R2(R−ΔR)2 or 1+ΔLL=1+2ΔRROr ΔLL=2ΔRR∴ (ΔR/R)(ΔL/L)= Contractional strain  Longitudinal strain =12