Question

A thin-walled capillary tube is suspended from the yoke of a balance and is counterpoised by weights. The lower end of the capillary tube is then brought into contact with the surface of water and an additional 0.135 g are needed to restore the balance. Find the radius of the capillary tube. The surface tension of water is 70 dyn/cm.

Answer 1

Answer: r ≅ 1.5 mm.

Explanation:

The surface tension acts on the inner and outer surfaces of the tube. Taking into account the thinness of the walls and assuming, in a first approximation, that the radii of cur-vature of the surface of the liquid at the walls of the capillary tube are of the same magnitude inside and outside the tube, we can take the forces acting at the inner and outer surfaces of the tube also to be equal. The force acting on the inner surface is equal to the weight of water which has risen in the tube because of the surface tension. The change in the weight of the capillary tube will be double this weight of water.