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Two rods of different materials having coefficients of thermal expansion α 1, α 2 and Young’s modulii Y 1, Y 2 respectively are fixed between two rigid massive walls. The rods are temperature. There is no bending of the rods. If α 1 :α 2= 2:3, the thermal stresses developed in the two rods are equal provided Y 1: Y 2 is equal to (a) 2:3 (b) 1:1 (c) 3:2 (d) 4:9

Two rods of different materials having coefficients of thermal expansion α1, α2 and Young’s modulii Y1,Y2 respectively are fixed between two rigid massive walls. The rods are temperature. There is no bending of the rods. If α12=2:3, the thermal stresses developed in the two rods are equal provided Y1:Y2 is equal to
(a) 2:3
(b) 1:1
(c) 3:2
(d) 4:9

Grade:upto college level

2 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
(c) ∆ℓ­ = ℓα∆T => ∆ℓ/ℓ = α∆T
Stress = Y * strain
∴ Stress = Yα∆T
For first rod stress = Y1α1∆T
For first rod stress = Y1α1∆T
For second rod stress = Y2α2∆T
Since, stress are equal
∴ Y1α1∆T = Y2α2∆T
Or, Y1/Y2 = α21 = 3/2
Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

∆ℓ­ = ℓα∆T
=> ∆ℓ/ℓ
= α∆T
Stress = Y * strain
∴ Stress = Yα∆T
For first rod stress = Y1α1∆T
For first rod stress = Y1α1∆T
For second rod stress = Y2α2∆T
Since, stress are equal
∴ Y1α1∆T = Y2α2∆T
Or, Y1/Y2 = α2/α1
= 3/2

Thanks and Regards

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