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Consider a narrow capillary tube dipped vertically into a large container of liquid with density and surface tension S . The liquid rises in the tube to a height h above the flat surface of the liquid in the container, forming a spherical meniscus. What is the radius of curvature R of this meniscus?

Options

  1. AR = S g h
  2. BR = 2S g h
  3. CR = g h 2S
  4. DR = S 2 g h

Correct answer

B. R = 2S g h

Step-by-step solution

The pressure difference across a spherical meniscus of radius of curvature R is given by P = 2S R . This pressure difference is balanced by the hydrostatic pressure of the liquid column of height h , which is P = g h . Equating the two expressions for the pressure difference: 2S R = g h Solving for R : R = 2S g h Answer: R = 2S g h

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