Q. Two rods of different materials having coefficient of thermal expansions $\alpha_{1}$ and $\alpha_{2}$ and Young’s moduli $Y_{1}$ and $Y_{2}$ respectively are fixed between two rigid walls. The rods are heated, such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_{1}$/$\alpha_{2}$=2/3 and stresses developed in the two rods are equal, then $\frac{Y1}{Y2}$ is
A) $3/2$
B) 1
C) $2/3$
D) $1/2$
Explanation
(a) Thermal stress is a measure of the internal distribution of force per unit area within body that is applied to the body, in the form of heat
Thermal stress=$Y\alpha\mathrm{\Delta}T$
Where Y is Young’s modulus, $\alpha$ the coefficient of linear expansion and $\mathrm{\Delta}T\ $the change in temperature
Both the rods are heated,
$\therefore$ $Y_{1}\alpha_{1}\mathrm{\Delta}T_{1} = Y_{2}\alpha_{2}\mathrm{\Delta}T_{2}$
Since, $\mathrm{\Delta}T_{1} = \mathrm{\Delta}T_{2}$
$\Rightarrow$ $\frac{Y_{1}}{Y_{2}} = \ \frac{\alpha_{2}}{\alpha_{1}} = \ \frac{3}{2}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.