A capillary tube of radius 1 mm is held vertical with the lower end in water. Determine the height of water raised in the capillary. If the length of the capillary tube is half of this calculated height, find the angle made by the water surface in the capillary with the wall.

Step-by-step solution

The height of water raised in a capillary tube is given by Jurin's law: h = 2T g r For water, assuming standard values T = 0.075 N/m , = 1000 kg/m ^3 , g = 10 m/s ^2 , and angle of contact = 0^ : h = 2 0.075 0^ 1000 10 10⁻³ = 0.015 m = 1.5 cm When the capillary tube is of insufficient length h' , the water rises to the top and the meniscus adjusts its angle of contact to ' such that the radius of curvature R changes, keeping h R constant. Since R = r , we have: h = h' ' Given that the new length is half of the calc