TS EAMCET · Physics · Thermal Properties of Matter
A piece of metal weighs \(45 \mathrm{~g}\) in air and \(25 \mathrm{~g}\) in a liquid of density \(1.5 \times 10^3 \mathrm{~kg}^{-3} \mathrm{~m}^{-3}\) kept at \(30^{\circ} \mathrm{C}\). When the temperature of the liquid is raised to \(40^{\circ} \mathrm{C}\), the metal piece weighs \(27 \mathrm{~g}\). The density of liquid at \(40^{\circ} \mathrm{C}\) is \(1.25 \times 10^3 \mathrm{~kg}-\mathrm{m}^{-3}\). The coefficient of linear expansion of metal is
- A \(1.3 \times 10^{-3} /{ }^{\circ} \mathrm{C}\)
- B \(5.2 \times 10^{-3} /{ }^{\circ} \mathrm{C}\)
- C \(2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}\)
- D \(0.26 \times 10^{-3} /{ }^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(2.6 \times 10^{-3} /{ }^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
The volume of the metal at \(30^{\circ} \mathrm{C}\) is \(\begin{aligned} V_{30} & =\frac{\text { loss of weight }}{\text { specific gravity } \times g} \\ & =\frac{(45-25) g}{1.5 \times g}=13.33 \mathrm{~cm}^3 \end{aligned}\) Similarly, volume of metal at…
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