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
IIT 1989, Medium
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(c) Thermal stress = $Y\alpha \Delta \theta $.
If thermal stress and rise in temperature are equal then
$Y \propto \frac{1}{\alpha }$ $\Rightarrow$ $\frac{{{Y_1}}}{{{Y_2}}} = \frac{{{\alpha _2}}}{{{\alpha _1}}} = \frac{3}{2}$
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