A thermometer bulb has volume $10^{-6} \mathrm{~m}^3$ and cross-section of the stem is $0.002 \mathrm{~cm}^2$. The bulb is filled with mercury at $0^{\circ} \mathrm{C}$. If the thermometer reads temperature as $100^{\circ} \mathrm{C}$, then the length of mercury column is (coefficient of cubical expansion of mercury $=18 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

To determine the height of the mercury column, consider the thermal expansion of mercury when heated from $0^\circ \mathrm{C}$ to $100^\circ \mathrm{C}$. The initial volume is $V_0 = 10^{-6} \mathrm{m}^3$, the cross-sectional area is $A = 2 \times 10^{-7} \mathrm{m}^2$, and the cubical expansion coefficient is $\gamma = 18 \times 10^{-5} \mathrm{/^{\circ}C}$.

The change in volume is given by $\Delta V = V_0 \gamma \Delta T = (10^{-6}) \times (18 \times 10^{-5}) \times 100 = 18 \times 10^{-9} \mathrm{m}^3$.

This volume occupies the stem, so $\Delta V = A L$. Solving for the length: $L = \frac{\Delta V}{A} = \frac{18 \times 10^{-9}}{2 \times 10^{-7}} = 9 \times 10^{-2} \mathrm{m} = 9 \mathrm{cm}$.

The correct answer is B.