Two rods of different materials having coefficients of linear expansion α1 and α2 and Young’s moduli, Y1 and Y2, respectively…

Q: Two rods of different materials having coefficients of linear expansion α1 and α2 and Young’s moduli, Y1 and 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 rods. If α12 = 2/3, then 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:

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

$\displaystyle Y_1 \alpha_1 = Y_2 \alpha_2$

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

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