A steel wire of length 4.5 m and a copper wire of length 3.5 m are stretched by the same amount under the same load. If the ratio of Young's modulus of steel to that of copper is 12/7, find the ratio of cross-sectional area of steel to that of copper.
Physics · Properties of solid and fluid
JEE Advanced

Question

A steel wire of length 4.5 m and a copper wire of length 3.5 m are stretched by the same amount under the same load. If the ratio of Young's modulus of steel to that of copper is 12/7, find the ratio of cross-sectional area of steel to that of copper.

Physics · Properties of solid and fluid

G1 Physics · Accepted Answer

Use stress σ=F/A, strain ε=ΔL/L and Young's modulus Y=σ/ε. For a uniform segment, ΔL=FL/(AY); for thermal restraint, thermal strain αΔT produces stress YαΔT. Substituting the given values gives 0.75.