Question

An iron rod of length $50\text{cm}$ is joined at an end to an aluminium rod of equal length to form a system. All measurements refer to ${20}^{\circ }C$. If coefficient of linear expension of iron and aluminium are $12\times {{10}^{-6}}^{\circ }C$ and $24\times {{10}^{-6}}^{\circ }C$ respectively, find average coefficient of linear expension of composite system?

• A. $36\times {{10}^{-6}}^{\circ }C$
• B. $20\times {{10}^{-6}}^{\circ }C$
• C. $24\times {{10}^{-6}}^{\circ }C$
• D. $38\times {{10}^{-6}}^{\circ }C$

Answer 1

The correct option is A $36\times {{10}^{-6}}^{\circ }C$

Change in length of iron rod
$\Delta L_i={\alpha }_i\Delta T$
Similarly
Change in length of aluminium rod
$\Delta L_a={\alpha }_a\Delta T$
Change in length of system
$\Delta L=\Delta L_i+\Delta L_a$
$=({\alpha }_i+{\alpha }_a)\Delta T$
$\therefore$ average coefficient of linear expension of composite system$=\frac{\Delta L}{\Delta T}=({\alpha }_i+{\alpha }_a)=12\times {{10}^{-6}}^{\circ }C+24\times {{10}^{-6}}^{\circ }C=36\times {{10}^{-6}}^{\circ }C$