Capillary rise | Mechanical properties of Solids | Grade 11 | Physics | Khan Academy

In this video, we dive deep into the fascinating phenomenon of capillary rise—why and how liquids rise in narrow tubes against gravity! 💧 0:00 – Introduction to capillary rise 0:10 – Water rises in a narrow tube: Observation 0:19 – Definition of capillary rise 0:29 – Cause: Adhesive vs cohesive forces 0:43 – Angle of contact explanation 1:02 – Understanding the curvature and rise 1:24 – Initial condition: t = 0 1:37 – Pressure difference causes rise 1:47 – Goal: Find height of capillary rise 2:01 – Introducing excess pressure formula (2σ/r) 2:24 – Relating bubble surface to capillary curvature 2:46 – Pressure difference: P_inside - P_outside = excess pressure 3:31 – Pressure at points inside/outside the meniscus 4:06 – Equating pressure at same horizontal level 4:19 – Pressure due to liquid column (ρgh) 4:44 – Substituting pressures into equation 5:33 – Final derivation: 2σ/r = ρgh 5:52 – Solving for h (height of capillary rise) 6:25 – Relating bubble radius r to capillary tube radius R 7:08 – Geometry: using cos(θ) to relate r and R 7:49 – Final formula: h = (2σ cosθ) / (ρgR) 8:16 – Summary and goodbye Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Chandan Ganotra