Capillarity in a glass tube (cohesion vs. adhesion): If the cohesion between fluid molecules exceeds the adhesion between the fluid and clean glass, what happens to the free liquid level inside a thin glass capillary dipped into the same liquid bath?

Introduction / Context:Capillarity describes how liquids rise or fall in narrow tubes due to the balance of surface tension forces and wetting behavior. Whether a liquid climbs (capillary rise) or depresses (capillary depression) depends on the relative magnitudes of cohesion (molecule–molecule attraction) and adhesion (liquid–solid attraction).

Given Data / Assumptions:

• Clean, wettable glass tube of small internal diameter.
• Fluid with cohesion greater than adhesion to glass (non-wetting on glass).
• Atmospheric conditions; static equilibrium; gravity acts downward.

Concept / Approach:

When adhesion > cohesion (e.g., water on clean glass), the meniscus is concave and the liquid rises. When cohesion > adhesion (e.g., mercury on glass), the meniscus is convex and the liquid level inside the tube is depressed relative to the reservoir. The vertical displacement is governed by surface tension and contact angle via the classical capillary relation h = (2 σ cos θ) / (ρ g r). For non-wetting liquids, θ > 90°, cos θ is negative, leading to a negative h (depression).

Step-by-Step Solution:

Verification / Alternative check:

Mercury in glass is the canonical example: cohesion dominates, producing a convex meniscus and a depressed column inside capillaries.

Why Other Options Are Wrong:

(a) describes capillary rise (adhesion-dominant); (b) would be true only if the tube were very wide (negligible capillarity); (d) viscosity does not set the static height; (e) no oscillatory static profile occurs.

Common Pitfalls:

Confusing dynamic wetting/viscosity with static capillary height; mixing up concave vs. convex menisci.

Final Answer:

lower than the outside free surface