Question

Two rods of different materials, having coefficients of linear expansions α₁ and α₂ and Young's modulli Y₁ and Y₂ are fixed between two rigid walls. The rods are heated to the same temperature. There is no bending of rods. If A₁ : A₂ = 2 : 3, find Y₁ : Y₂ when equal thermal stress is developed in the two rods.

Answer 1

Increase in length due to thermal expansion, when temperature of the rod of length L increase by θ, is

ΔL = α L θ;

Strain = ΔL/L = α θ

As Y = Stress/Strain = S/α θ

or Y ∞ 1/α because S and θ are constants for the two rods in this question.

Hence, Y₁/Y₂ = α₂/α₁ = 3/2