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

• A

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

• B

  ${\mathrm{l}}_1^2{\mathrm{\alpha }}_2={\mathrm{l}}_2^2{\mathrm{\alpha }}_1$

• C

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

• D

  ${\mathrm{l}}_1{\mathrm{\alpha }}_2^2={\mathrm{l}}_2{\mathrm{\alpha }}_1^2$