A glass rod of radius `r_(1)` is inserted symmetrically into a vertical capillary tube of radius `r_(2)` such that their lower ends are at the same level. The arrangement is now dipped in water. Find the height to which water will rise in to the tube.
(S = surface tension of water, d= density of water).

Explanation

Total upward force due to surface tension
`=S[2pir_(1)+2pir_(2)]" "...(1)`
This supports the weight of the liquid column of height h.
Weight of liquid column
`=h[pir_(2)^(2)-pir_(1)^(2)]rhog" "...(2)`
Equating (1) and (2),
`hpi(r_(2)+r_(1))(r_(2)-r_(1))rhog=2piS(r_(1)+r_(2))orh(r_(2)-r_(1))rhog=2S`
`thereforeh=(2S)/((r_(2)-r_(1))rhog)`