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).

A glass rod of radius r_(1) is inserted symmetrically into a vertical

1.	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).
Answer» Solution :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)`