Two rods of different materials have lengths $\ell_1$ and $\ell_2$ whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

• A
  $\alpha_1^2 \ell_1 = \alpha_2^2 \ell_2$
• B
  $\frac{\ell_1}{\ell_2} = \frac{\alpha_2}{\alpha_1}$
• C
  $\frac{\ell_1}{\ell_2} = \frac{\alpha_1}{\alpha_2}$
• D
  $\ell_1^2 \alpha_2 = \ell_2^2 \alpha_1$