A copper wire of cross sectional area A is under a tension F. Young's modulus of copper is γ and Poisson's ratio σ. Then find the fractional change in its cross sectional area.

(3)Stress  S=F/ALongitudinal  strain  ε=Sγ=FAγNow,    Δr/rΔl/l=−σ  ⇒  Δrr=−σ.Δll=−σεNow,   A=πr2∴   ΔAA=2.Δrr=−2σε∴    Fractional  decrease  in  its  cross  sectional  area=  2σε  = 2σFAY.