Capillary Rise

NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids) explains capillary action through the equation $h=\frac{2T\cos \theta }{r\rho g}$, 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 $T$, $\theta$, $\rho$ and $g$ are unchanged, $h\propto 1/r$. Halving the radius therefore doubles the height: $h^{\prime }=2\times 8=16\text{cm}$. 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.