A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

Options

A.
B.
C.
D.

Explanation

To solve the problem of comparing the liquid columns in two identical capillary tubes, one dipped in water and the other in a soap-water solution, we can follow these steps:

### Step 1: Understand Capillary Action
Capillary action occurs due to the interplay of cohesive and adhesive forces in a liquid. When a liquid is in contact with a solid surface (like the walls of a capillary tube), the adhesive forces between the liquid and the solid can cause the liquid to rise in the tube.

### Step 2: Identify the Liquids
- **Tube A**: Dipped in water.
- **Tube B**: Dipped in a soap-water solution.

### Step 3: Analyze Surface Tension
Surface tension plays a crucial role in capillary action. Water has a relatively high surface tension, while soap-water solutions have a lower surface tension due to the presence of surfactants.

### Step 4: Apply the Capillary Rise Formula
The height of the liquid column (h) in a capillary tube can be described by the formula:
\[ h = \frac{2T \cos \theta}{R \rho g} \]
Where:
- \( T \) = surface tension of the liquid
- \( \theta \) = contact angle
- \( R \) = radius of the tube
- \( \rho \) = density of the liquid
- \( g \) = acceleration due to gravity

### Step 5: Compare the Two Tubes
- For **Tube A (water)**: Water has a higher surface tension, leading to a certain height of rise.
- For **Tube B (soap-water solution)**: The surface tension is lower, which means the height of the liquid column will be less compared to that in tube A.

### Step 6: Conclusion
Since the surface tension of the soap-water solution is lower than that of water, the liquid column in Tube A (water) will rise higher than in Tube B (soap-water solution). Therefore, the relative heights of the liquid columns will show that Tube A has a higher liquid column than Tube B.

### Final Answer
The correct option is that the liquid column in Tube A (water) will be higher than the liquid column in Tube B (soap-water solution).

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