Question

Asteel wire of length 4.7 m and cross-sectional area 3.0 × 10^–5m²stretches by the same amount as a copper wire of length 3.5 m andcross-sectional area of 4.0 × 10^–5m²under a given load. What is the ratio of the Young’s modulus ofsteel to that of copper?

Answer 1

Length of the steelwire, L₁ = 4.7 m

Area of cross-sectionof the steel wire, A₁ = 3.0 × 10^–5m²

Length of the copperwire, L₂ = 3.5 m

Area of cross-sectionof the copper wire, A₂ = 4.0 × 10^–5m²

Change in length = ΔL₁= ΔL₂ = ΔL

Force applied in boththe cases = F

Young’s modulusof the steel wire:

… (i)

Young’s modulusof the copper wire:

Dividing (i) by(ii), we get:

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