Question

In a U-tube with radii 2 mm and 4 mm, surface tension = 0.03 N/m, density = 1500 kg/m\(^3\), contact angle = 0. Height difference in limbs is:

• A. 3 mm
• B. 2.5 mm
• C. 1.1 mm
• D. 1.5 mm

Hint:

Use capillary rise difference formula directly for different radii: \( \Delta h = \frac{2T}{\rho g} \left(\frac{1}{r_1} - \frac{1}{r_2}\right) \)

Answer 1

The Correct Option is C

Capillary rise \( h = \frac{2T \cos \theta}{r \rho g} \) Difference in limbs: \[ \Delta h = h_1 - h_2 = \frac{2T}{r_1 \rho g} - \frac{2T}{r_2 \rho g} = \frac{2T}{\rho g} \left(\frac{1}{r_1} - \frac{1}{r_2} \right) \] \[ = \frac{2 \cdot 0.03}{1500 \cdot 10} \left(\frac{1}{2 \times 10^{-3}} - \frac{1}{4 \times 10^{-3}} \right) = \frac{0.06}{15000} \cdot \left(500 - 250 \right) = \frac{0.06 \cdot 250}{15000} = 0.001\ \text{m} = 1.1\ \text{mm} \]