Iron has coefficient of linear expansion of $12 \times 10^{- 6} / {}^{0}C$ and copper has coefficient of linear expansion of $18 \times 10^{- 6} / {}^{0}C$ . An iron rod and a copper rod differ in lengths by 5 cm at all temperatures, then their lengths expressed in cm must respectively be

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10, 15

20, 15

15, 10

25, 20

answer is B.

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Detailed Solution

$l_{1} α_{1} = l_{2} α_{2}$
$l_{1} \times 12 \times 10^{- 6} = l_{2} \times 18 \times 10^{- 6}$
$2 l_{1} = 3 l_{2} \to (1) \Rightarrow l_{1} > l_{2}$
$l_{1} - l_{2} = 5 l_{1} - \frac{2 l_{1}}{3} = 5$
$l_{1} = 15 c m l_{2} = 10 c m$

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