Question

Two rods of different materials having coefficients of linear expansion ${\alpha }_1$ and ${\alpha }_2$ and Young's moduli, $Y_1$ and $Y_2$, 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 rods. If ${\alpha }_1/{\alpha }_2=2/3$, then 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. $4:9$

Answer 1

Answer: (C)

$3:2$

Thermal stress = Y(Thermal strain)=$Y\times \alpha \Delta T$
Thus, since $\Delta T$ is same, for stresses to be equal, $Y_1{\alpha }_1=Y_2{\alpha }_2$
Thus, $\frac{Y_1}{Y_2}=\frac{{\alpha }_2}{{\alpha }_1}=3:2$