The lengths of two metallic rods at temperatures $θ$ are $L_{A} and L_{B}$ and their linear coefficient of expansion are $α_{A} and α_{B}$ respectively. If the difference in their lengths is to remain constant at any temperature then

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$α_{A} α_{B} = 1$

$\frac{L_{A}}{L_{B}} = \frac{α_{A}}{α_{B}}$

$α_{A} = α_{B}$

$\frac{L_{A}}{L_{B}} = \frac{α_{B}}{α_{A}}$

answer is B.

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Detailed Solution

Change in $L_{A}$ = change in $L_{B}$

i.e., $∆ L_{A} = L_{B}$

$\Rightarrow α_{A} ∆ {TL}_{A} = α_{B} ∆ {TL}_{B}$

or $α_{A} L_{A} = α_{B} L_{B}$

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