Question

Two rods of lengths $l_1$ and $l_2$ are made of materials whose coefficients of linear expansion are ${\alpha }_1$ and ${\alpha }_2$. If the difference between the two lengths is independent of temperature, then

• A. $\frac{l_1}{l_2}=\frac{{\alpha }_1}{{\alpha }_2}$
• B. $\frac{l_1}{l_2}=\frac{{\alpha }_2}{{\alpha }_1}$
• C. $l_2^2{\alpha }_1=l_1^2{\alpha }_2$
• D. $\frac{{\alpha }_1^2}{l_1}=\frac{{\alpha }_2^2}{l_2}$

Answer 1

The correct option is B $\frac{l_1}{l_2}=\frac{{\alpha }_2}{{\alpha }_1}$

$L_1=l1[1+{\alpha }_1\Delta T]L_2=l2[1+{\alpha }_2\Delta T]L_1+L_2=(l_1+l2)+\left(\Delta T\right)(l_1{\alpha }_1-l_2{\alpha }_2)If{L}_1-L_{2}istobeindependentof\Delta T,then{l}_1{\alpha }_1-l_2{\alpha }_2=0\Rightarrow \frac{l_1}{l2}=\frac{{\alpha }_1}{{\alpha }_2}\frac{l_1}{l2}=\frac{{\alpha }_2}{{\alpha }_1}$