Q. Two rods, one of aluminium and the other made of steel, having initial length $l_{1}$ and $l_{2}$ are connected together to form a single rod of length $l_{1}$+$l_{2}$. The coefficients of linear expansion for aluminium and steel are $\alpha_{a}$ and $\alpha_{s}$ respectively. If the length of each rod increases by the same amount when their temperature are raised by $t℃$, then find the ratio $\frac{l_{1}}{(l_{1} + l_{2})}$.
A) $\frac{\alpha_{s}}{\alpha_{a}}$
B) $\frac{\alpha_{a}}{\alpha_{s}}$
C) $\frac{\alpha_{s}}{(\alpha_{a} + \alpha_{s})}$
D) $\frac{\alpha_{a}}{(\alpha_{a +}\alpha_{s})}$
Explanation
(c) Given, $\mathrm{\Delta}l_{1} = \mathrm{\Delta}l_{2}$
Or $l_{1}\alpha_{a}t = l_{2}\alpha_{s}t$
$\therefore$ $\frac{l_{1}}{l_{2}} = \frac{\alpha_{s}}{\alpha_{a}}$
Or $\frac{l_{1}}{l_{1} + l_{2}} = \ \frac{\alpha_{s}}{\alpha_{a} + \alpha_{s}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.