Q: Two rods of different material having coefficients 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 roads 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: Thermal Stress $\large \sigma = Y \alpha \Delta \theta $

$\large \sigma_1 = \sigma_2 $

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

$\large \frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1}= \frac{3}{2}$