Question

Two uniform rods AB and BC have Young's modulii $1.2\times {10}^{11}N/m^2\text{and}1.5\times {10}^{11}N/m^2$ respectivey. If coefficient of linear expansion of AB is $1.5\times {10}^{-5}/°C$ and both have equal area of cross section, then coefficient of linear expansion of BC, for which there is not shift of the junction at all temperatures, is

• A. $1.5\times {10}^{-5}/°C$
• B. $1.2\times {10}^{-5}/°C$
• C. $0.6\times {10}^{-5}/°C$
• D. $0.75\times {10}^{-5}/°C$

Answer 1

The correct option is B $1.2\times {10}^{-5}/°C$

$Y_{AB}=1.2\times {10}^{11}N/m^2,Y_{BC}=1.5\times {10}^{11}N/m^2$
For no shift of junction at all temperatures, the elongation due to temperature rise must compensate the elongation due to strain.

$\Rightarrow \alpha L\Delta T=\frac{FL}{AY}$

$or,\alpha \propto \frac{1}{Y}$ [ for a given rise/change in temperature]

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

Substituting the values,

$\frac{1.5\times {10}^{-5}}{{\alpha }_2}=\frac{1.5\times {10}^{11}}{1.2\times {10}^{11}}$

$or,{\alpha }_2=1.2\times {10}^{-5}/{}^{\circ }C$

Why this question? Concepts: It tests your understanding of stress development due to change in temperature of rod.