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 = `sigma[2pir_(1)+2pir_(2)]`
This supports the weight of the liquid column of height h.
Weight of liquid column = `h=[pir_(2)^(2)-pir_(1)^(2)]rhog`
Equating, `hpi(r_(2)+r_(1))(r_(2)-r_(1))rhog=2pisigma(r_(1)+r_(2))(or)h(r_(2)-r_(1))rhog=2sigma(or)h=(2sigma)/((r_(2)-r_(1))rhog)`