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?
Given Data,
Length of the steel wire, Ls = 4.7 m
Area of cross-section of the steel wire, As = 3.0 × 10-5 m2
Length of the copper wire, Lc = 3.5 m
Area of cross-section of the steel wire, Ac = 4.0 × 10-5 m2
Consider the force applied in both the cases is = Fs = Fc = F
Change in Length = ΔLs = ΔLc = ΔL (since both the wires stretch by the same amount)
Young's modulus ( E ) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
Formula for young’s modulus for steel:
…………… (1)
Formula for young’s modulus for steel:
Yc = 
Yc = 
………… (2)
Dividing (1) by (2)
= 
Cancelling the common terms F and
ΔL, the equation changes to,
= 
⇒ 
Hence, the ratio of Young’s modulus of steel to that of copper is 1.79:1.
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
