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Two rods of lengths $L_{1}$ and $L_{2}$ are made of materials whose coefficients of linear expansion are $α_{1}$ and $α_{2}$ . If the difference between the two lengths is independent of temperature.

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$α_{1}^{2} L_{1} = α_{2}^{2} L_{2}$

$\frac{L_{1}}{L_{2}} = \frac{α_{1}}{α_{2}}$

$\frac{L_{1}}{L_{2}} = \frac{α_{2}}{α_{1}}$

$L_{1}^{2} α_{1} = L_{2}^{2} α_{2}$

answer is B.

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Detailed Solution

From the expression $e = Lα (∆ θ)$

$e_{1} = L_{1} α_{1} = L_{2} α_{2}$

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