# The Lengths Of Steel And Copper Rods Are So That The Length Of The Steel Rod Is 5 Cm Longer Than That Of The Copper Rod At All Temperatures. What Will Be The Length Of Each Rod?

Sol:

Let Ls and Lc be the lengths of the steel and copper rods.

Let αs and αc be the coefficients of linear expansion.

When the rods are heated by Δ t°C, the increase in length of the steel rod and the copper rod is:

⇒ ΔLs = LαΔ T

⇒ ΔLc = Lαs Δ T

Given:Ls – Lc = 5 cm for all Δ T.

⇒ Ls αs Δ  T = Lc αΔ T

$\Rightarrow \frac{L_{s}}{L_{c}} = \frac{\alpha_{c}}{\alpha_{s}} = \frac{1.7 * 10^{-5}}{1.1 * 10^{-5}}$

⇒ Ls = $\frac{17L_{c}}{11}$

Now by using Ls – Lc = 5, we get Lc = 9.17 cm.

Therefore, Ls= 5 + 9.17 = 14.17 cm.

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