TS EAMCET · Physics · Thermal Properties of Matter
Two metal rods \(\mathrm{A}\) and \(\mathrm{B}\) each of length \(50 \mathrm{~cm}\) and diameter \(4.0 \mathrm{~mm}\) are joined together at temperature \(30^{\circ} \mathrm{C}\). What is the change in length of the combined rod at \(230^{\circ} \mathrm{C}\) ? [Given linear expansion coefficients of rods A and B are respectively, \(2.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}\) and \(\left.1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right]\)
- A 4 mm
- B 2 mm
- C 3 mm
- D 1 mm
Answer & Solution
Correct Answer
(C) 3 mm
Step-by-step Solution
Detailed explanation
\begin{aligned} & \Delta l=\Delta l_{\mathrm{A}}+\Delta l_{\mathrm{B}} \\ & =l_{\mathrm{A}} \alpha_{\mathrm{A}} \Delta \mathrm{T}+l_{\mathrm{B}} \alpha_{\mathrm{B}} \Delta \mathrm{T} \\ & =0.5 \times 200 \times\left(2 \times 10^{-5}+1 \times 10^{-5}\right) \\ & =100 \times 3…
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