The following is the question that very commonly appears in all HS textbooks.
A hollow sphere with a hole is taken to a depth of 40cm when the water starts entering the hole. if the surface tension of water is 70dyne per cm find the radius of the hole.
All the textbooks solve it in a similar manner as given below:- When water enters the sphere, radius of the bubble of air formed, will be equal to radius of the hole say r. Then excess pressure inside the bubble equals the external pressure at the depth of 40cm and thus on equating 2T/r to h*d*g, they find the answer.
but i dont find this explanation satisfying at all. why should a bubble form only at that depth and that too of the radius of hole. cant it form at any depth and the radius depend on the depth with maximum being equal to the radius of the hole.?