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. ${\alpha }_1{l}_2={\alpha }_2{l}_1$
• B. ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$
• C. ${\alpha }_1^2{l}_2={\alpha }_2^2{l}_1$
• D. ${\alpha }_1{l}_1={\alpha }_2{l}_2$

Answer 1

Answer: (D)

${\alpha }_1{l}_1={\alpha }_2{l}_2$

Both the rods will have same change in length.

$\Rightarrow \Delta l_1=\Delta l_2$

$\Rightarrow l_1{\alpha }_1\Delta T=l_2{\alpha }_2\Delta T$

$\Rightarrow l_1{\alpha }_1=l_2{\alpha }_2$