Q: Two rods of different materials having coefficient of thermal expansion α_{1}, α_{2} and Young’s moduli Y_{1}, Y_{2} 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 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

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} $