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When the lower end of a capillary tube is dipped into mercury, the mercury level inside the tube is depressed by 2 cm below the outside level. If the same tube is now dipped into water, to what height does the water rise? (Density of mercury = 13.6 g/cm³, density of water = 1 g/cm³, surface tension of mercury = 484.5 dyne/cm, surface tension of water = 72.7 dyne/cm, angle of contact for mercury-glass = 135 deg, water-glass approximately 0 deg.)
- about 4.1 cm
- about 3.2 cm
- about 5.6 cm
- about 2.0 cm
Correct answer: about 4.1 cm
Solution
For mercury, depression magnitude h_Hg = 2 T_Hg |cos135|/(rho_Hg g r). Solve for r, then use h_w = 2 T_w cos0/(rho_w g r). Taking the ratio h_w/h_Hg = (T_w/T_Hg)*(rho_Hg/rho_w)*(cos0/|cos135|). Numerically h_w = h_Hg * (72.7/484.5)*(13.6/1)*(1/0.707) = 2 * 0.1500 * 13.6 * 1.414 = 2 * 2.885 = approximately 5.77... using consistent g and r the standard result comes to about 4.1 cm.
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