Answer :
A capillary tube A is dipped in water, another identical capillary tube B is dipped in soap- water solution, the following shows the relative nature of the liquid columns in the two tubes is D) A higher then B.
The relative nature of the liquid columns in the two capillary tubes can be determined by comparing the capillary rise in each tube.
The height of liquid rise in a capillary tube is given by the formula:
[tex]\[ h = \frac{{2\gamma \cdot \cos(\theta)}}{{\rho \cdot g \cdot r}} \][/tex]
Where:
- h is the height of the liquid rise,
- [tex]\( \gamma \)[/tex] is the surface tension of the liquid,
- [tex]\( \theta \)[/tex] is the contact angle between the liquid and the solid surface of the tube (which is assumed to be zero for complete wetting),
- [tex]\( \rho \)[/tex] is the density of the liquid,
- g is the acceleration due to gravity, and
- r is the radius of the capillary tube.
Since the tubes are identical, the radius r will be the same for both tubes.
Comparing the heights of liquid rise in the two tubes, we need to consider the surface tensions of water and soap-water solution:
For tube A (dipped in water), [tex]\( \gamma_A = 0.025 \, \text{N/m} \).[/tex]
For tube B (dipped in soap-water solution), [tex]\( \gamma_B = 0.073 \, \text{N/m} \).[/tex]
As the surface tension of the soap-water solution is higher than that of water, the capillary rise in tube B will be less than in tube A.
So, the relative nature of the liquid columns in the two tubes is that the liquid column in tube A (water) will rise higher compared to the liquid column in tube B (soap-water solution).
The correct answer is D) A higher then B.
Note: The question was incomplete, the complete question: "A capillary tube A is dipped in water. Another identical capillary tube B is dipped in soap- water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? Consider the surface tension of soap solution and water to be 0.073 N/m and 0.025 N/m respectively at room temperature. A) A as high as B, B) A as low as B, C) B higher then A, and D) A higher then B."
