A long capillary tube of radius `r = 1 mm` open at both ends is filled with water and placed vertically. What will be the height (in `cm`) of the column of water left in the capillary walls is negligible. (surface tension of water is `72 "dyne"//"cm"` and `g = 1000 "cm"//"sec"^(2)`)

Answer

`2.8cm`

Explanation

Weight of liquid `=` surface tension force
`pir^(2)hdg = alpha2pir`
`h = (2alpha)/(dgr)`
work done by surface tension force `= (alpha. 2pir)h = (4pialpha^(2))/(dg)`
potential energy liquid `= mg h//2 = pir^(2)h dg '(alpha)/(dgr) = (2pialpha^(2))/(dg)`
rest part of work done
i.e. `[(4pialpha^(2))/(dg)-(2pialpha^(2))/(dg)=(2pialpha^(2))/(dg)]` is lost the form of heat.