Question

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

• 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 A $\frac{l_1}{l_2}=\frac{{\alpha }_1}{{\alpha }_2}$

increase the length of first rod

$△L_1=L_1{\propto }_1\theta$

increase the length of second rod

$△L_2=L_2{\propto }_2\theta$

${ L }_{ 1 }{ \propto }_{ 1 }\theta $

$=L_2{\propto }_2\theta$

$\frac{L_1}{L_2}=\frac{{\propto }_1}{{\propto }_2}$