Question

A glass capillary tube of internal radius \(r = 0.25\,\text{mm}\) is immersed in water. The top end of the tube is projected by \(2\,\text{cm}\) above the surface of the water. At what angle does the liquid meet the tube? (Surface tension of water \(=0.7\,\text{N/m}\)).

• A. \(\theta = 90^\circ\)
• B. \(\theta = 70^\circ\)
• C. \(\theta = 45^\circ\)
• D. \(\theta = 35^\circ\)

Hint:

For capillarity: \[ h\propto \cos\theta \] Larger contact angle reduces rise.

Answer 1

The Correct Option is B

Step 1: Capillary rise formula: \[ h=\frac{2T\cos\theta}{\rho g r} \]
Step 2: Given \(h=2\,\text{cm}=0.02\,\text{m}\), \(T=0.7\,\text{N/m}\), \(r=0.25\times10^{-3}\,\text{m}\), \(\rho=1000\,\text{kg/m}^3\), \(g=10\,\text{m/s}^2\).
Step 3: Substitute values: \[ 0.02=\frac{2(0.7)\cos\theta}{1000\times10\times0.25\times10^{-3}} \]
Step 4: Solving: \[ \cos\theta \approx 0.34 \Rightarrow \theta \approx 70^\circ \]