The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. Determine the depression of the mercury column in the capillary. Furthermore, if the length dipped inside is half of this depression, find the angle made by the mercury surface at the end of the capillary with the vertical. The surface tension of mercury is 0.465 N/m and the contact angle of mercury with glass is 135^ .

Step-by-step solution

The formula for the capillary depression h of a liquid is given by: h = 2T (180^ - ) g r Substituting the given values ( T = 0.465 N/m , = 135^ , = 13600 kg/m ^3 , g = 9.8 m/s ^2 , r = 10⁻³ m ): h = 2 0.465 45^ 13600 9.8 10⁻³ h = 0.93 1 2 133.28 0.00493 m = 4.93 mm When the tube is dipped to a depth l which is less than the natural depression h , the mercury meniscus stays at the lower end of the tube and adjusts its contact angle to a new value ' to balance the pressure. The new depth is related to ' by: l = 2T (1