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A steel rod and a copper rod have lengths $L_{s}$ and $L_{c}$ respectively at a certain temperature. It is found that the difference between their lengths remains constants at all temperatures. If $α_{s} a n d α_{c}$ are their respective coefficients of linear expansion, the ratio $L_{s} / L_{c}$ is given by

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$(1 + \frac{α_{c}}{α_{s}})$

$(1 + \frac{α_{s}}{α_{c}})$

$\frac{α_{s}}{α_{c}}$

$\frac{α_{c}}{α_{s}}$

answer is D.

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Detailed Solution

When the rods are heated by $∆$ t °C, the increase in length of the steel rod and the copper rod are

$∆ L_{s} = L_{s} α_{s} ∆ t ∆ L_{c} = L_{c} α_{c} ∆ t$

The difference between their lengths will remain constant at all temperatures if $∆ L_{s} = ∆ L_{c}$ , i.e. if

$L_{s} α_{s} ∆ t = L_{c} α_{c} ∆ t o r \frac{L_{s}}{L_{c}} = \frac{α_{c}}{α_{s}}$

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