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Two rods of different materials having coefficients of linear expansion $\alpha_1, \alpha_2$ 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 $\alpha_1: \alpha_2=2: 3$, the thermal stresses developed in the two rods are equally provided $Y_1: Y_2$ is equal to
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$3: 2$
Thermal stress $=Y \alpha \Delta \theta$.
If thermal stress and rise in temperature are equal then $Y\propto \frac{1}{\alpha} \Rightarrow \frac{I_1}{I_2}=\frac{\alpha_2}{\alpha_1}=\frac{3}{2}$
If thermal stress and rise in temperature are equal then $Y\propto \frac{1}{\alpha} \Rightarrow \frac{I_1}{I_2}=\frac{\alpha_2}{\alpha_1}=\frac{3}{2}$
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