TS EAMCET · Physics · Thermal Properties of Matter
The length of a metal rod at \(30^{\circ} \mathrm{C}\) is \(30 \mathrm{~cm}\). If its temperature is raised to \(105^{\circ} \mathrm{C}\), its length is increased by \(0.027 \mathrm{~cm}\). Then the coefficient of linear expansion of the metal is
- A \(12 \times 10^{-4} /{ }^{\circ} \mathrm{C}\)
- B \(12 \times 10^{-5} /{ }^{\circ} \mathrm{C}\)
- C \(12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)
- D \(12 \times 10^{-7} /{ }^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
Coefficient of linear expansion, \[ \begin{aligned} & \alpha=\frac{\Delta \mathrm{L}}{\mathrm{L} \Delta \mathrm{T}} \\ & =\frac{0.027}{30 \times(105-30)}=\frac{0.027}{30 \times 75}=12 \times 10^{-6} /{ }^{\circ} \mathrm{C} \end{aligned} \]
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