Q137 / 160 · TS EAMCET 2019 (03 May Shift 1) · Physics
The area of a circular copper coin increases by $0.4 \%$ when its temperature is raised by $100^{\circ} \mathrm{C}$. The coefficient of linear expansion of the coin is :
- A$1 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
- Correct answerB$2 \times 10^{-5} / \mathrm{C}$
- C$3 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
- D$4 \times 10^{-5} / \mathrm{C}$
Solution
Given, area of a circular copper coin increases by $0.4 \%$.
i.e., $\quad \frac{\Delta A}{A}=0.004$
Increase in temperature, $\Delta T=100^{\circ} \mathrm{C}$
We lonow that, the coefficient of areal expansion $\beta$ is given by
$$
\beta=\left(\frac{\Delta A}{A}\right) \cdot \frac{1}{\Delta T}=\frac{0.004}{100}=4 \times 10^{-5} / \mathrm{C}
$$
$\therefore$ Coefficient of linear expansion, of the coin is
$$
\alpha=\frac{\beta}{2}=\frac{4 \times 10^{-5}}{2} / \mathrm{C}=2 \times 10^{-5} / \mathrm{C}
$$
Hence, the correct answer is option: 'B'.