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.
• B.
• C.
• D.

Answer 1

The correct option is B

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