Q60 / 75 · VITEEE 2021 · Physics
The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and in a steel ${ }^6 /{ }^{\circ} \mathrm{C}$, then that of glass is
- Correct answerA$9 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
- B$6 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
- C$36 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
- D$27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
Solution
$$
\begin{aligned}
& \gamma_{\text {real }}=\gamma_{\text {app. }}+\gamma_{\text {vessel }} \\
& \text { So }\left(\gamma_{\text {app. }}+\gamma_{\text {vessel }}\right)_{\text {glass }}=\left(\gamma_{\text {app }}+\gamma_{\text {vessel }}\right)_{\text {steel }} \\
& \Rightarrow 153 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {glass }} \\
& =144 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {steel }}
\end{aligned}
$$
Further,
$$
\begin{aligned}
& \left(\gamma_{\text {vessel }}\right)_{\text {steel }}=3 \alpha=3 \times\left(12 \times 10^{-6}\right) \\
& \quad=36 \times 10^{-6} /{ }^{\circ} \mathrm{C} \\
& \Rightarrow 153 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {glass }} \\
& =144 \times 10^{-6}+36 \times 10^{-6} \\
& \Rightarrow\left(\gamma_{\text {vessel }}\right)_{\text {glass }}=3 \alpha=27 \times 10^{-6} /{ }^{\circ} \mathrm{C} \\
& \Rightarrow \alpha=9 \times 10^{-6} /{ }^{\circ} \mathrm{C}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.