Question

A capillary tube of radius \( r \) is dipped in water; find the height \( h \) to which water rises if the surface tension is \( T \).

• A. \( \dfrac{T}{\rho g r} \)
• B. \( \dfrac{2T}{\rho g r} \)
• C. \( \dfrac{4T}{\rho g r} \)
• D. \( \dfrac{T}{2\rho g r} \)

Hint:

Capillary rise is inversely proportional to the radius of the tube. Narrower tubes cause higher rise of liquid.

Answer 1

The Correct Option is B

Concept: Capillary rise occurs due to surface tension. The upward force due to surface tension balances the weight of the liquid column. The formula for capillary rise is \[ h = \frac{2T\cos\theta}{\rho g r} \] For water in a glass tube, the angle of contact \( \theta = 0^\circ \).
Step 1: {Substitute \( \cos 0^\circ = 1 \).} \[ h = \frac{2T}{\rho g r} \]
Step 2: {Final expression for height of capillary rise.} \[ h = \frac{2T}{\rho g r} \]