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# 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 α1:α2=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

Navjyot Kalra
7 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
one year ago
Dear Student,

∆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