What causes the height of capillary rise to be inversely proportional to the tube’s radius?
The capillary rise formula (h = 2Scosθ/ρgr) shows that h is inversely proportional to radius (r) because the pressure difference due to surface tension (2S/r) must balance the weight of the liquid column, which depends on h.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.