In to a vessel containing pure water a clean glass tube of radius 3.6 10⁻⁴ ~m is held vertically with 12 cm of the tube above the water level. Now the capillary tube is moved down in to the water so that only 2 cm of its length is above the water surface. Angle of contact at this position is (given surface tension of water =7.2 10⁻² Nm ⁻¹ and g=10 ~ms ⁻² )

Step-by-step solution

The capillary rise h in a tube of radius r is given by the formula h = 2T r g , where T is the surface tension, is the angle of contact, is the density of water, and g is the acceleration due to gravity. First, calculate the maximum capillary rise h_ max for pure water in a glass tube, where = 0^ and 0^ = 1 . Given T = 7.2 10⁻² N/m , r = 3.6 10⁻⁴ m , = 1000 kg/m ^3 , and g = 10 m/s ^2 : h_ max = 2 7.2 10⁻² 3.6 10⁻⁴ 1000 10 = 14.4 10⁻² 3.6 10^0 = 4 10⁻² m = 4 cm . When the tube is pushed down such that only 2 cm is