UPCET / UPSEE Capillarity — practice questions

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Capillarity questions and exercises with answers

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The phenomenon of rise (or fall) of a liquid in a narrow capillary tube is called:Read the answer and worked solution →A capillary tube of radius $r$ dipped in a liquid of surface tension $T$ and density $\rho$, contact angle $\theta$, gives rise (or fall) to height $h$ where:Read the answer and worked solution →

Worked practice questions

The phenomenon of rise (or fall) of a liquid in a narrow capillary tube is called:

Capillarity
Viscosity
Surface tension only
Buoyancy

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Correct answer: A. Capillarity

Capillarity = the net effect of surface tension + adhesive/cohesive forces. Water rises in glass capillaries (cohesive < adhesive — wets) mercury falls (cohesive > adhesive — doesn't wet).

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A capillary tube of radius $r$ dipped in a liquid of surface tension $T$ and density $\rho$, contact angle $\theta$, gives rise (or fall) to height $h$ where:

$h = 2T \cos\theta / (r \rho g)$
$h = T \cos\theta / (r \rho g)$
$h = r \rho g / (2T \cos\theta)$
$h = 2 T r / (\rho g \cos\theta)$

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Correct answer: A. $h = 2T \cos\theta / (r \rho g)$

**Force balance:** $\pi r^2 h \rho g = 2\pi r T \cos\theta$ ⇒ $h = 2T \cos\theta / (r\rho g)$. Narrower tube ⇒ greater rise. If $\theta > 90°$ (non-wetting like mercury–glass), $\cos\theta < 0$ ⇒ capillary depression.