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?


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

[latex]\Rightarrow \frac{L_{s}}{L_{c}} = \frac{\alpha_{c}}{\alpha_{s}} = \frac{1.7 * 10^{-5}}{1.1 * 10^{-5}}[/latex]

⇒ Ls = [latex] \frac{17L_{c}}{11}[/latex]

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

Therefore, Ls= 5 + 9.17 = 14.17 cm.

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