A uniform wire (Young's modulus 2 × 1 0 11 Nm − 2 ) is subjected to longitudinal tensile stress of 5 × 1 0 7 Nm − 2 . If the overall volume change in the wire is 0.02% , the fractional decrease i

Question

A uniform wire (Young's modulus 2 × 1 0 11 Nm − 2 ) is subjected to longitudinal tensile stress of 5 × 1 0 7 Nm − 2 . If the overall volume change in the wire is 0.02% , the fractional decrease in the radius of the wire is close to:

TestHub · Accepted Answer

Given, y = 2 × 1 0 11 Nm − 2 ​ Stress ( A F ​ ) = 5 × 1 0 7 Nm − 2 Δ V = 0.02% = 2 × 1 0 − 4 m 3 r Δ r ​ = ? ​ ​ γ = strain stress ​ ⇒ strain ( ℓ 0 ​ Δ ℓ ​ ) = stress γ ​ Δ V = 2 π r ℓ 0 ​ Δ r − π r 2 Δ ℓ ​ From eqns (i) and (ii) putting the value of Δ ℓ , ℓ 0 ​ and Δ V and solving we get r Δ r ​ = 0.25 × 1 0 − 4

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