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

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$3:2$

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(D) The thermal stress $\sigma$ developed in a rod fixed between two rigid walls when heated by a temperature change $\Delta T$ is given by the formula: $\sigma = Y \alpha \Delta T$.Given that the thermal stress in both rods is equal,we have: $\sigma_1 = \sigma_2$.Substituting the formula for thermal stress: $Y_1 \alpha_1 \Delta T = Y_2 \alpha_2 \Delta T$.Since the temperature change $\Delta T$ is the same for both rods,we can cancel it from both sides: $Y_1 \alpha_1 = Y_2 \alpha_2$.Rearranging the terms to find the ratio $Y_1 : Y_2$: $\frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1}$.Given the ratio $\alpha_1 : \alpha_2 = 2 : 3$,we have $\frac{\alpha_1}{\alpha_2} = \frac{2}{3}$,which implies $\frac{\alpha_2}{\alpha_1} = \frac{3}{2}$.Therefore,$\frac{Y_1}{Y_2} = \frac{3}{2}$.

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