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Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. It arises due to the cohesive forces between liquid molecules. This concept explains why small objects like insects can walk on water and why droplets form spheres.

At the molecular level, the molecules at the surface of the liquid are not surrounded by similar molecules on all sides. Instead, they are pulled inwards by molecules deeper inside the liquid. This results in a tension on the surface, acting like a stretchy film. This force per unit length is what we identify as surface tension, denoted as \( T \) and measured in Newton per meter (N/m).

In the context of the exercise, surface tension is responsible for the liquid's ability to climb up the walls of the capillary tube. Given the surface tension of \( 0.072 \, \mathrm{N/m} \), it aids in calculating the height of capillary rise.

The capillary rise phenomenon involves a liquid rising or falling in a small tube due to surface tension. The Capillary Rise Formula helps calculate this height. When the contact angle \( \theta \) is zero, indicating a wetting situation, the liquid uniformly sticks to the surface.

The formula is given by:

• \[ h = \frac{2T}{\rho g r_{\text{effective}}} \]

where:

• \( h \) - the height of the liquid rise (m)
• \( T \) - surface tension of the liquid (N/m)
• \( \rho \) - density of the liquid (kg/m³)
• \( g \) - acceleration due to gravity (m/s²)
• \( r_{\text{effective}} \) - effective radius (m)

For the exercise, substituting values into the formula shows how the capillary's diameter and rod's diameter affect the rise to \( 1.44 \, \mathrm{cm} \). By using the formula correctly, you determine how high the liquid will climb in any similar experiment.

The meniscus is the curve at the liquid's surface where it meets the side of the container. In capillary tubes, the shape of the meniscus is largely influenced by the liquid's adhesive forces with the tube’s material.

For a liquid like water in a glass capillary, the meniscus is concave because the adhesive forces between water molecules and glass are stronger than the cohesive forces among water molecules. This is why water climbs up the sides of the tube, forming a "U" shape at the top.

In the exercise, a meniscus is formed as the liquid rises up the annular space due to zero contact angle. The arrangement, therefore, produces a cylindrical meniscus along the inner walls of the capillary. The meniscus assists in understanding how liquids can rise or fall in narrow spaces. This unique property is crucial to the way capillary action operates.