The height of the liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is 5 cm. If the same tube is dipped in similar way in another liquid B of surface tensio

Question

The height of the liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is 5 cm. If the same tube is dipped in similar way in another liquid B of surface tension and density double the values of liquid A , the height of liquid column raised in liquid B is (Assume that angle of contact for both the liquids is almost same)

TestHub · Accepted Answer

The height of the liquid column in a capillary tube is given by $h = \frac{2 T cos θ}{r ρ g}$

For liquid $A$ , $h_{A} = \frac{2 T _{A} cos θ}{r ρ _{A} g} = 5$ cm

For liquid $B$ , the surface tension is $T_{B} = 2 T_{A}$ and the density is $ρ_{B} = 2 ρ_{A}$

The height of the liquid column for liquid $B$ is:

$h_{B} = \frac{2 T _{B} cos θ}{r ρ _{B} g} = \frac{2 ( 2 T _{A} ) cos θ}{r ( 2 ρ _{A} ) g} = \frac{2 T _{A} cos θ}{r ρ _{A} g} = h_{A}$

$h_{B} = 5$ cm $= 0.05$ m

Answer: $0.05$ m

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