The coefficient of linear expansion of steel and brass are $11 \times 10^{- 6} /^{o} C$ and $19 \times 10^{- 6} /^{o} C$ respectively. If their difference in lengths at all temperatures has to be kept constant at 30 cm, their lengths at $0^{0} C$ should be

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92 cm, 62 cm

83 cm, 52 cm

71.25 cm, 41.25 cm

62.25 cm. 32.25 cm

answer is B.

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Detailed Solution

$\begin{aligned} ℓ_{1} = \frac{{xα}_{2}}{(α_{1} - α_{2})} \\ ℓ_{s} = \frac{30 \times 19 \times 10^{- 6}}{8 \times 10^{- 6}} \end{aligned}$
= 71.25 cm
$ℓ_{b} = \frac{30 \times 11 \times 10^{- 6}}{8 \times 10^{- 6}}$
= 41.25 cm

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