Question

Two rods of lengths $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are ${\alpha }_1$ and ${\alpha }_2$ respectively. If the difference between the two lengths is independent of temperature, then choose the correct option.

• A. $\left(L_1/L_2\right)=\left({\alpha }_1/{\alpha }_2\right)$
• B. $\left(L_1/L_2\right)=\left({\alpha }_2/{\alpha }_1\right)$
• C. $L_1^2{\alpha }_1=L_2^2{\alpha }_2$
• D. ${\alpha }_1^2{L}_1={\alpha }_2^2{L}_2$

Answer 1

The correct option is B $\left(L_1/L_2\right)=\left({\alpha }_2/{\alpha }_1\right)$

Since difference between the two lengths is independent of temperature,
$\Delta L_1=\Delta L_2$
$L_1{\alpha }_1\Delta \theta =L_2{\alpha }_2\Delta \theta$ or $\left(\frac{L_1}{L_2}\right)=\left(\frac{{\alpha }_2}{{\alpha }_1}\right)$
Hence, the correct answer is option (b).