The rods of length $L_1$ and $L_2$ are made of materials 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
    $\frac{L_1}{L_2} = \frac{\alpha_1}{\alpha_2}$
  • 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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Two rods of different metals have coefficients of linear expansion $\alpha_1$ and $\alpha_2$ respectively. Their respective lengths are $L_1$ and $L_2$. At all temperatures,$(L_2 - L_1)$ remains the same. The correct relation is:

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