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MHT CET · Physics · Thermal Properties of Matter

Two rods, one of aluminium and the other of steel, having initial lengths ' \(\mathrm{L}_1\) ' and ' \(\mathrm{L}_2\) ' are connected together to form a single rod of length \(\left(\mathrm{L}_1+\mathrm{L}_2\right)\). The coefficients of linear expansion of aluminium and steel are ' \(\alpha_1\) ' and ' \(\alpha_2\) ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by \({ }^{\prime} t^{\circ} \mathrm{C}\), then the ratio \(\frac{\mathrm{L}_1}{\mathrm{~L}_1+\mathrm{L}_2}\) will be

  1. A \(\frac{\alpha_2}{\alpha_1}\)
  2. B \(\frac{\alpha_1}{\alpha_2}\)
  3. C \(\frac{\alpha_2}{(\alpha_1+\alpha_2)}\)
  4. D \(\frac{\alpha_1}{(\alpha_1+\alpha_2)}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\alpha_2}{(\alpha_1+\alpha_2)}\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{ll} & \text {Given } \Delta \mathrm{L}_1=\Delta \mathrm{L}_2 \Rightarrow \mathrm{~L}_1 \alpha_1 \mathrm{t}=\mathrm{L}_2 \alpha_2 \mathrm{t} \\ \therefore \quad & \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\alpha_2}{\alpha_1} \Rightarrow \frac{\mathrm{~L}_1}{\mathrm{~L}_1+\mathrm{L}_2}=\frac{\alpha_2}{\alpha_1+\alpha_2}\end{array}\)