Question

A steel wire of length 4.7 m and cross-sectional area 3.0 × 10^–5 m² stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10^–5 m² under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Answer 1

Length of the steel wire, L₁ = 4.7 m
Area of cross-section of the steel wire, A₁ = 3.0 × 10^–5 m²
Length of the copper wire, L₂ = 3.5 m
Area of cross-section of the copper wire, A₂ = 4.0 × 10^–5 m²
Change in length = ΔL₁ = ΔL₂ = ΔL
Force applied in both the cases = F
Young’s modulus of the steel wire:

The ratio of Young’s modulus of steel to that of copper is 1.79: 1.