First slide

Surface tension

Question

The lower end of a vertical glass capillary tube of radius 2r is dipped in water. Now a solid glass rod of radius r is coaxially inserted into the tube. It surface tension of water is T and density of water is $ρ$ , then capillary rise (h) is

Difficult

A

$\frac{3 T}{2 ρrg}$
B

$\frac{2 T}{ρrg}$
C

$\frac{4 T}{ρrg}$
D

$3 T / ρrg$

Solution

Mass of water in the space between the tube and the rod
$m = π [{(2 r)}^{2} - {(r)}^{2}] ρh = 3 {πr}^{2} . ρh$
vertically upward tension force acting on the water column = $2 πrT + 2 π (2 r) T = 6 πrT$
In equilibrium, $3 {πr}^{2} ρhg = 6 πrT \Rightarrow h = \frac{2 T}{rρg}$

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