Capillary Rise on Depression in a Small Diameter Tube

The correct answer is option 'C': The capillary rise on depression in a small diameter tube is inversely proportional to the diameter. Let's understand why this is the correct answer.

Capillary Rise
Capillary rise refers to the phenomenon of a liquid rising or being depressed in a narrow tube or capillary. It occurs due to the intermolecular forces between the liquid molecules and the solid surface of the tube.

Influence of Tube Diameter
The capillary rise is inversely proportional to the diameter of the tube. This means that as the diameter of the tube decreases, the capillary rise increases. Conversely, as the diameter of the tube increases, the capillary rise decreases.

Surface Tension
Surface tension is the property of a liquid's surface that allows it to resist external forces. It is caused by the cohesive forces between the liquid molecules. Surface tension plays a significant role in capillary rise.

Influence of Surface Tension
The capillary rise is directly proportional to the surface tension of the liquid. This means that as the surface tension of the liquid increases, the capillary rise also increases. Similarly, if the surface tension decreases, the capillary rise decreases.

Relationship between Diameter and Capillary Rise
The relationship between the tube diameter and capillary rise can be explained by considering the forces involved. The capillary rise is caused by the balance between the adhesive forces between the liquid and the tube and the cohesive forces within the liquid.

When the tube diameter is small, the adhesive forces dominate over the cohesive forces, leading to a higher capillary rise. This is because the liquid molecules experience a higher attraction to the solid surface of the tube. As a result, the liquid rises or is depressed more in the tube.

On the other hand, when the tube diameter is large, the cohesive forces within the liquid become more significant compared to the adhesive forces. This reduces the capillary rise as the liquid molecules experience less attraction to the tube surface.

Therefore, the capillary rise is inversely proportional to the diameter of the tube. A smaller tube diameter results in a higher capillary rise, while a larger tube diameter leads to a lower capillary rise.

Conclusion
In summary, the capillary rise on depression in a small diameter tube is inversely proportional to the diameter. This relationship is due to the dominance of adhesive forces over cohesive forces in a small diameter tube, resulting in a higher capillary rise.