Two rods of different materials, having coefficients of linear expansi

1.	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» 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

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»

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