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What is the gain in potential energy of the water column in case of rise of water in glass capillary tube? What is the work done by surface tension ? Assume that the angle of contact between glass and water is 0^@. |
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Answer» Solution :Rise of WATER inside the capillary tube of RADIUS r is, `h=(2Tcos theta)/(rho g r)=(2T)/(rho gr)` [ where T = SURFACE TENSION, `theta=` angle of contact`0^@` ,`rho` = density of water ] Mass of watercolumn of height `h, m =pir^2 h rho` The height of centre of mass of the water column `=h/2` `therefore` The gain in potential energy, `U=mgxxh/2=1/2 pi r^2 rho gh^2` `=1/2pi r^2 rho g xx (4T^2)/(rho^2g^2r^2)=(2piT^2)/(rhog)` The work done by surface tension, `W2pi r h Tcos theta=2pi r xx(2T)/(rho g r)xxTxxcos0^@=(4pi T^2)/(rho g)` |
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