Capillarity in tubes – effect of tube size on rise/depression With an increase in the size (radius) of a capillary tube, the rise or depression of the liquid column due to surface tension will:

Introduction:Capillary action causes rise or depression of liquids in narrow tubes due to surface tension and contact angle. The magnitude depends strongly on tube radius.

Given Data / Assumptions:

• Tube is circular and clean; contact angle is characteristic of the liquid–solid pair.
• Gravitational acceleration is constant.
• Isothermal conditions for short observation times.

Concept / Approach:The capillary rise formula is h = (2 * sigma * cos(theta)) / (rho * g * r) where sigma is surface tension, theta is contact angle, rho is density, g is gravity, and r is tube radius. Thus h is inversely proportional to r.

Step-by-Step Solution:1) Recognize that h ∝ 1/r.2) If r increases, 1/r decreases.3) Therefore, the capillary rise (or depression magnitude) decreases.

Verification / Alternative check:In very large tubes (r → large), the capillary effect becomes negligible, consistent with everyday observation that buckets or pipes of large diameter do not show visible capillary rise.

Why Other Options Are Wrong:

• Increase: contradicts inverse relation with r.
• Remain unchanged: ignores dependence on radius.
• Depend only on liquid temperature: temperature affects sigma, but radius remains a direct factor.

Common Pitfalls:Confusing rise with meniscus curvature; forgetting contact angle sign can cause depression (e.g., mercury).

Final Answer:decrease