Question

A capillary tube of radius r is lowered into liquid of of surface tension T and density Ro .Then work done by surface tension will be?

Answer 1

Height raised  

h = 2Tcos θ/ rρg

As θ = 0, cos θ = 1  

therefore h = 2T/rρg  

Work done by surface tension  

W = T × 2πr × h  

W = T × 2πr × 2T rρg

W = 4πT2/ρg

Answer 2

Hey dear,

◆ Answer-
W = 4πT^2 / ρg

◆ Solution-
Let h be the height of liquid column which can be calculated by-
h = 2T / (ρrg)

Force at surface tension is
F = T × 2πr

Work done by surface tension is calculated by-
Work = Force × displacement
W = T × 2πr × 2T / ρrg
W = 4πT^2 / ρg

Therefore, work done by surface tension is 4πT^2 / ρg .

Hope this helps..