Question

If two soap bubbles of different radii are connected by a tube, then:
(A) air flows from the bigger bubble to the smaller bubble till size becomes equal.
(B) air flows from the bigger bubble to the smaller bubble till sizes are interchangeable.
(C) air flows from smaller bubble to bigger
(D) there is no flow of air.

Answer 1

Hint
From the formula for the pressure inside a bubble, $ P = {P_o} + \dfrac{{4S}}{R} $ we can see as the radius decreases the pressure increases. So, the bubbles will try to acquire a larger volume to decrease pressure. So, the bigger bubble will grow in size and the smaller bubble will reduce in size.

Complete step by step answer
 A soap bubble has two surfaces, the outer and the inner surface of the bubble. There is a pressure difference between these two surfaces and the surface tension balances this pressure difference. The pressure inside the bubble is always greater than the outside.
 The pressure inside a soap bubble is given by the formula,
 $ P = {P_o} + \dfrac{{4S}}{R} $ where $ R $ is the radius of the bubble.
From here, we can see that the pressure is inversely proportional to the radius,
 $ P \propto \dfrac{1}{R} $
Hence, as the size of the soap bubble increases the pressure inside the bubble decreases.
So the soap bubble will always try to acquire a larger size to decrease the pressure inside it.
Now when two bubbles of different radii are connected with a tube, then the larger bubble will try to grow even larger to decrease pressure.
Therefore, the air will flow from the smaller bubble to inside the larger bubble, and the larger bubble will grow at expense of the smaller bubble until the smaller bubble vanishes completely. Thus the air flows from the smaller bubble to the bigger bubble.
Hence, the correct answer is option (C).

Note
When two bubbles of different radii are connected, the pressure inside the bubbles causes the larger bubble to grow even larger and the smaller bubble to shrink down till it vanishes.