Question

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $ l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures, which one of the following relations holds good ?

• A. $\alpha_1 l^2_2 = \alpha_2 l_1^2$
• B. $\alpha_1^2 l_2 = \alpha_2^2 l_1$
• C. $\alpha_1 l_1 = \alpha_2 l_2$
• D. $\alpha_1 l_2 = \alpha_2 l_1$

Answer 1

Answer: (C)

Change in length for both rods should be same
$\Delta \ell_1 = \Delta \ell_2$
$\ell_1 \alpha_1 \Delta T = \ell_2 \alpha_2 \Delta T$
$\ell_1 \alpha_1 = \ell_2 \alpha_2$