Two rods of lengths $l_{1} a n d l_{2}$ are made of materials whose coefficients of linear expansion are $α_{1} a n d α_{2}$ respectively. If the difference between the two lengths is independent of temperature, then

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

$l_{1}^{2} α_{2} = l_{2}^{2} α_{1}$

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

$l_{1} α_{2}^{2} = l_{2} α_{1}^{2}$

answer is A.

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Detailed Solution

$l_{1}^{'} = l_{1} (1 + α_{1} t) l_{2}^{'} = l_{2} (1 + α_{2} t) l_{1}^{'} - l_{2}^{'} = l_{1} - l_{2} + (l_{1} α_{1} - l_{2} α_{2}) t l_{1} α_{1} = l_{2} α_{2}$

For the difference to be independent of temperature

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