Question

When a capillary tube is dipped in a liquid, the liquid rises to a height h in the tube. The free liquid surface inside the tube is hemispherical in shape. The tube is now pushed down so that the height of the tube outside the liquid is less than h. Then
(A) The liquid will come out of the tube like in a small fountain.
(B) The liquid will ooze out of the tube slowly.
(C) The liquid will fill the tube but not come out of its upper end.
(D) The free liquid surface inside the tube will not be hemispherical.

Answer 1

Hint : It is given that a capillary tube is dipped into the water tub, the water rises to a height h in the tube. Now it is said that the tube is further pushed inside the tub, so that the undipped part height is lesser than h. Now, it is essential to understand that due to capillarity and surface tension , the liquid will be held and rather won’t come out of the tube. Using this , find the appropriate choice.

Complete step by step answer
Before understanding the crux of the problem, let us understand the properties of fluid. Among all the properties of fluid, surface tension and capillarity. Surface tension is an extensive property of fluids that allows the fluid molecules to resist external force, due to the cohesion between the molecules. Now, Capillarity is defined as the property of fluid to rise or depress in a passage tube having some cross-sectional area, when the fluid experiences force on it. Due to fluid viscosity and surface tension, the capillarity property occurs.
Now, let us assume a capillary tube of given radius is getting immersed inside a liquid , which has a surface tension . When the tube is immersed, the liquid will start to rise on the tube to a certain height which can be mathematically given as:
 $ \Rightarrow h = \dfrac{{2T}}{{r\rho g}} $
Where T is the surface tension of the fluid , r is assumed to be the radius of the meniscus formed on the tube and $ \rho $ to be the density of the fluid.
When the capillary tube is immersed further, h value is getting increased, which reduces the radius since the height of water in the capillary tube is inversely proportional to radius of the meniscus. This shows that, as height increases, the hemispherical radius of the meniscus decreases and hence the water will become flatter.
Due to the existence of surface tension and capillarity, the water won’t overflow. This means that option (a) and (b) are out and options (c) and (d) are the right answers.

Note
As the tube is pushed down and as the water level in the tube rises, the angle of contact at the liquid surface inside the tube will change in a way that surface tension caused along the walls of the tube nullifies the weight produced by the liquid column.