Two rods of different materials having coefficient of thermal expansion α1, α2 and Young’s moduli Y1, Y2 respectively…..

Q: Two rods of different materials having coefficient of thermal expansion α1, α2 and Young’s moduli Y1, Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in 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

Ans: (c)

Sol:

$ \displaystyle Y_1 \alpha_1 \Delta \theta = Y_2 \alpha_2 \Delta \theta $

$ \displaystyle Y_1 \alpha_1 = Y_2 \alpha_2 $

$ \displaystyle \frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1} $

$ \displaystyle \frac{Y_1}{Y_2} = \frac{3}{2} $

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