Two rods of different material having coefficients of thermal expansion α1 , α2 and young’s moduli Y1, Y2 respectively…

Q: Two rods of different material having coefficients 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 roads are equal provided Y1 : Y2 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 $

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