Q 11-10-020NEETJEE MainEAMCET 2009 (Medical)Easy
The volume of mercury in the bulb of a thermometer is $10^{-6}\ \text{m}^3$. The area of cross-section of the capillary tube is $2 \times 10^{-7}\ \text{m}^2$. If the temperature is raised by $100°$C, the increase in the length of the mercury column is ($\gamma_{Hg} = 18 \times 10^{-5}\ °\text{C}^{-1}$)
Answer: (C) $9$ cm
Concept. The extra mercury volume $\Delta V = V\gamma\Delta T$ goes up the capillary: $\Delta l = \dfrac{\Delta V}{A}$.
Step 1. Volume increase.
$$\Delta V = 10^{-6} \times 18 \times 10^{-5} \times 100 = 1.8 \times 10^{-8}\ \text{m}^3$$
Step 2. Rise in the column.
$$\Delta l = \frac{1.8 \times 10^{-8}}{2 \times 10^{-7}} = 0.09\ \text{m} = 9\ \text{cm}$$
Answer. $9$ cm (Option C).
Solution by Sreeraj P, M.Sc Physics