Capillary Rise

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Water rises to a height of 8 cm in a clean glass capillary tube; if a second capillary tube of half the radius is used in the same water, the new rise will be approximately:

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NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids) explains capillary action through the equation $h = \dfrac{2T\cos	heta}{rho g}$, where the height of rise is inversely proportional to the tube radius for a given liquid. Surface tension pulls the liquid up the narrow tube until the upward force balances the weight of the raised column. Since $T$, $	heta$, $ho$ and $g$ are unchanged, $h \propto 1/r$. Halving the radius therefore doubles the height: $h' = 2 	imes 8 = 16\ 	ext{cm}$. The option 8 cm wrongly assumes rise is independent of radius. The option 4 cm incorrectly treats height as directly proportional to radius. The option 32 cm mistakenly applies an inverse-square relation rather than the correct inverse-first-power dependence. As a plausibility check, narrower tubes are known to lift water higher (as seen in thin soil pores and plant xylem), so an increase from 8 cm to 16 cm is consistent with everyday capillary behaviour.

Capillary Rise

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