Question

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

The correct option is C $3:2$

$Given{\alpha }_1:{\alpha }_2=2:3$
From the formula of Thermal Stress given above,we can see that it is proportional to $\alpha$, $\theta$ and $Y$.
$Given$: Thermal Stress developed in the two rods are equal and both rods undergo the same change in temperature.
So we can write that,
$Y_1{\alpha }_1=Y_2{\alpha }_2$
$\frac{Y_1}{Y_2}=\frac{{\alpha }_2}{{\alpha }_1}$
$\frac{Y_1}{Y_2}=3:2$