Question

If a capillary tube of radius $r$ is immersed in a liquid, the liquid rises to a height $h$. The corresponding mass of liquid column is $m$. The mass of water that would rise in another capillary tube of twice the radius is

• A. $2m$
• B. $5m$
• C. $3m$
• D. $4m$
• E. $\frac{m}{2}$

Hint:

In capillary rise problems, mass varies directly with radius.

Answer 1

The Correct Option is A

Concept: Capillary rise: \[ h = \frac{2T \cos\theta}{\rho g r} \] So, \[ h \propto \frac{1}{r} \] Mass of liquid column: \[ m = \rho \times \text{Volume} = \rho \times (\pi r^2 h) \]

Step 1: Substitute $h \propto \frac{1}{r}$: \[ m \propto r^2 \cdot \frac{1}{r} = r \]

Step 2: If radius doubles: \[ r' = 2r \] \[ m' \propto 2r = 2m \] Final Answer: \[ m' = 2m \]