Surface Tension Capillary Rise Method — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Surface Tension (Capillary Rise Method) Valid for liquids in narrow tubes where the meniscus can be approximated as a hemisphere. Requires static equilibrium. Assume the liquid rises to height h in the tube due to surface tension. Identify the upward force: The vertical component of surface tension acting along the circumference of the meniscus is F up = T 2 pi r cos(theta). Identify the downward force: The weight of the liquid column of height h is F down = mass g = (Volume rho) g = (pi r 2 h rho) g. At equilibrium, equate F up = F down: T 2 pi r cos(theta) = pi r 2 h rho g. Solve for T: T = (r h rho g) / (2 cos(theta)). The tube radius r must be very small compared to the height h. The capillary tube must be clean and of uniform bore. The liquid temperature must remain constant (as T depends on temp). Angle of contact theta must be accurately known. Confusing the radius of the capillary tube (r) with the radius of the meniscus (R). They are related by r = R cos(theta). Assuming the liquid inside the meniscus (the small curved volume) is always negligible; derived formula usually ignores it, but correction factors exist. Thinking water always rises; if theta > 90 degrees (e.g., Mercury), h is negative (depression). Forgetting to convert mm or cm to SI unit meters.