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MHT CET202611 April 2026Evening ShiftPhysicsMechanical Properties of FluidsActual

In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' is inserted symmetrically and one end of the combination is dipped vertically in water such that lower end of the capillary and thin wire are at same level. If 'T' is the surface tension of water and ' ' is the density of water then the rise of water in the capillary is

Options

  1. AT (R-r) g
  2. B2T (R-r) g
  3. C4T (R+r) g
  4. DT (R+r) g

Correct answer

B. 2T (R-r) g

Step-by-step solution

The upward force due to surface tension acts on the inner circumference of the capillary tube and the outer circumference of the inserted wire. Assuming the angle of contact to be zero, the total upward force is given by: F = T(2 R) + T(2 r) = 2 T(R + r) The volume of the water raised in the annular space between the capillary and the wire is: V = (R^2 - r^2)h The weight of the raised water column is: W = V g = (R^2 - r^2)h g In equilibrium, the upward force due to surface tension balances the weight of the water c

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