Question

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 \(=18 \times 10^{-5} /{ }^{\circ} \mathrm{C}\) )

• A. 90 cm
• B. 9 mm
• C. 9 cm
• D. 0.9 mm

Hint:

The rise of mercury in the stem equals the volume expansion divided by the stem cross-section.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The extra volume of mercury is \(\Delta V = V\gamma\Delta T\).
This extra volume rises in the narrow stem.

Step 2: Volume Expansion
\(\Delta V = 10^{-6}\times 18\times 10^{-5}\times 100 = 1.8\times 10^{-8}\ \text{m}^3\)
In cubic centimetres this is \(1.8\times 10^{-2}\ \text{cm}^3\).

Step 3: Calculation
Length \(= \dfrac{\Delta V}{A} = \dfrac{1.8\times 10^{-2}}{0.002} = 9\ \text{cm}\)

Final Answer:
The mercury column is 9 cm long. \[ \boxed{\text{(C) }9\text{ cm}} \]