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(C) The thermal stress $\sigma$ developed in a rod fixed between two rigid walls when heated by a temperature change $\Delta 	heta$ is given by the f

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$3:2$

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(C) The thermal stress $\sigma$ developed in a rod fixed between two rigid walls when heated by a temperature change $\Delta 	heta$ is given by the formula:$\sigma = Y \alpha \Delta 	heta$where $Y$ is the Young's modulus and $\alpha$ is the coefficient of linear expansion.Given that the thermal stresses are equal $(\sigma_1 = \sigma_2)$ and the increase in temperature $\Delta 	heta$ is the same for both rods,we have:$Y_1 \alpha_1 \Delta 	heta = Y_2 \alpha_2 \Delta 	heta$$Y_1 \alpha_1 = Y_2 \alpha_2$Rearranging the terms to find the ratio $Y_1 : Y_2$:$\frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1}$Given $\alpha_1 : \alpha_2 = 2 : 3$,we have $\frac{\alpha_1}{\alpha_2} = \frac{2}{3}$,which implies $\frac{\alpha_2}{\alpha_1} = \frac{3}{2}$.Therefore,$\frac{Y_1}{Y_2} = \frac{3}{2}$ or $Y_1 : Y_2 = 3 : 2$.

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