Question

Two rods of different materials having coefficients of linear expansions ${\alpha }_1$ and ${\alpha }_2$ and young's modulus of elasticity $Y_1$ and $Y_2$ respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature without bending. If ${\alpha }_1:{\alpha }_2=2:3,$ then the thermal stress developed in the two rods will be equal if $Y_1:Y_2$ is equal to

• A. $2:3$
• B. $3:2$
• C. $1:1$
• D. $4:9$

Answer 1

The correct option is B $3:2$

The thermal stress developed in rod = $Y\alpha \left(\Delta T\right)$

For the same rise of temperature $(\Delta T$), the thermal stress is equal,
$Y_1{\alpha }_1\Delta T=Y_2{\alpha }_2\Delta T$
$\Rightarrow Y_1{\alpha }_1=Y_2{\alpha }_2$
$\Rightarrow \frac{Y_1}{Y_2}=\frac{{\alpha }_2}{{\alpha }_1}$
$Y_1:Y_2={\alpha }_2:{\alpha }_1$
$Y_1:Y_2=3:2$