JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at \(30^{\circ} C\). The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6} /{ }^{\circ} C\) and \(1.2 \times 10^{-5} /{ }^{\circ} C\), respectively. The length of this composite rod when its temperature is raised to \(100^{\circ} C\), is _________ cm .
- A 120.20 cm
- B 120.15 cm
- C 120.03 cm
- D 120.06 cm
Answer & Solution
Correct Answer
(B) 120.15 cm
Step-by-step Solution
Detailed explanation
\(\ell_{\text {final }}=\ell_0\left(1+\alpha_{ A } \Delta T \right)+\ell_0\left(1+\alpha_{ B } \Delta T \right)\) \(=\ell_0\left[2+\left(\alpha_{ A }+\alpha_{ B }\right) \Delta T \right]\) \(=60\left[2+\left(36 \times 10^{-6}\right) \times 70\right]\) \(=60[2+0.0025]\)…
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