The rods of length $L_1$ 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 temperatures

  • A

    $\left( {\frac{{{L_1}}}{{{L_2}}}} \right) = \left( {\frac{{{\alpha _1}}}{{{\alpha _2}}}} \right)$

  • B

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

  • C

    $L_1^2{\alpha _1} = L_2^2{\alpha _2}$

  • D

    $\alpha _1^2{L_1} = \alpha _2^2{L_2}$

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