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Coefficient of linear expansion of brass and steel rods are $α_{1} and α_{2}$ . Lengths of brass and steel rods are $l_{1} and l_{2}$ respectively. If $(l_{2} - l_{1})$ is maintained same at all tempera-tures, which one of the following relations holds good?

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$α_{1} 1_{2}^{2} = α_{2} 1_{1}^{2}$

$α_{1} l_{2} = α_{2} l_{1}$

$α_{1} l_{1} = α_{2} l_{2}$

answer is D.

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Detailed Solution

$∆ l_{1} = ∆ l_{2}$ because they expand equally

$l_{1} α_{1} ∆ t = l_{2} α_{2} ∆ t$

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