A stress of 9.8 × 10⁶ N/m² is applied to a wire and Young’s modulus is 10^11 N/m² find the percentage increase in length

Question

A stress of 9.8 × 10⁶ N/m² is applied to a wire and Young’s modulus is 10¹¹ N/m² find the percentage increase in length [Ans. 0.0098%]

Answer

Stress = 9.8 × 10⁶ N/m²

Young’s modulus = 10¹¹ N/m²

Young modulus = stress \over strain

⇒ strain = stress \over Young\ modulus

⇒ strain = 9.8 × 10^6 \over 10^11

⇒ Δl\over l = 0.000098

Percentage increase in length = Δl\over l×100

= 0.000098 × 100

= 0.0098 %