Question

Water rises to a height 3 cm in a capillary tube. If cross-sectional area of capillary tube is reduced to \( \frac{1}{10} \)th of initial area then water will rise to a height of

• A. 9 cm
• B. 6 cm
• C. 7 cm
• D. 8 cm

Hint:

The height of water in a capillary tube is inversely proportional to the radius, so reducing the cross-sectional area increases the rise.

Answer 1

The Correct Option is A

Step 1: Understanding the capillary rise.
The height to which liquid rises in a capillary tube is given by the formula: \[ h = \frac{2T}{\rho g r} \] where \( T \) is the surface tension, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( r \) is the radius of the capillary tube.
Step 2: Effect of the cross-sectional area.
Since the capillary rise depends on the radius of the tube, and the radius \( r \) is related to the cross-sectional area \( A \) by \( A = \pi r^2 \), reducing the area by a factor of 10 will increase the height by a factor of \( \sqrt{10} \). Therefore, the new height is \( 3 \times \sqrt{10} \approx 9 \, \text{cm} \).
Step 3: Conclusion.
The correct answer is (A), 9 cm.