Question

Two rods of different materials having coefficients of linear expansion ${\alpha }_1,{\alpha }_2$ and Young's modulii $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. The rods are heated such that they undergo the same increases in temperature. There is no bending of rods. If ${\alpha }_1:{\alpha }_2=2:3$. the thermal stress 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)

$3:2$

$Y=\frac{FL}{A\Delta l}$

$\frac{\Delta l}{L}=\alpha \Delta T$

$F=\frac{YA\Delta l}{L}=YA\alpha \Delta T$

$Y_{1}A{\alpha }_1\Delta T=Y_{2}A{\alpha }_2\Delta T$

$\frac{{\alpha }_1}{{\alpha }_2}=\frac{Y_2}{Y_1}$

$\frac{2}{3}=\frac{Y_1}{Y_2}$

$\frac{Y_1}{Y_2}=\frac{3}{2}$