alleryThe height to which a liquid rises in a capillary tube of radius r is (with surface tension T, contact angle θ, density ρ):
Ah = 2 T cosθ / (r ρ g)
Bh = T cosθ / (r ρ g)
Ch = T sinθ / (r ρ g)
Dh = ρ g r / (2 T cosθ)
Answer & Solution
Correct answer: A. h = 2 T cosθ / (r ρ g)
1. Balance upward surface-tension force around the meniscus circumference with weight of the lifted liquid.
2. Upward force = T cosθ · 2π r.
3. Weight of lifted column = ρ g h · π r².
4. Equate: h = 2 T cosθ / (r ρ g).
5. So h is inversely proportional to r — narrower tubes lift higher (mercury depresses, since cosθ < 0).
_Source: syllabus Physics Ch 9 §9.8 Capillary Rise_
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