Question

Two bubbles A and B (A > B) are joined through a narrow tube. Then
A. The size of A will increase
B. the size of B will increase
C. the size of B will increase until the pressure equals
D. none of these

Answer 1

Hint: We are given the two bubbles of different radii which are joined through a narrow tube. With the help of the formula of pressure inside a bubble $P={{P}_{0}}+\dfrac{4S}{R}$ we see that if the radius increases, pressure decreases. So the larger bubble will try to grow more in size by reducing the size of the smaller bubble.

Formula used:
The pressure inside the soap bubble is given by
$P={{P}_{0}}+\dfrac{4S}{R}$
Where R is the radius of the bubble, $S$ is the surface tension and $P_0$ is the atmospheric pressure.

Complete step by step solution:
We know a soap bubble has two surfaces, the outer surface and the inner surface. There exists a pressure difference between these two pressures and the pressure inside the bubbles is always greater than the pressure outside the bubble. The pressure inside the soap bubble is given by,
$P={{P}_{0}}+\dfrac{4S}{R}$
We can see that the $P\propto \dfrac{1}{R}$. That is P is inversely proportional to R Hence as the size of the soap bubble increases the pressure inside the bubble decreases. So the bubble always tries to get a large size by decreasing the pressure inside the bubble.

Now when we are given two bubbles A and B which are joined through a narrow tube, then the larger bubble (A) tries to increase its size by decreasing the pressure. Therefore, the air will flow from the smaller bubble ( B ) to the larger bubble (A) and the size of the larger bubble (A) increases.

Thus, option A is the correct answer.

Note: Remember that when the two bubbles of different radius are joined, the pressure inside the bubble causes the bubble to expand more and the smaller bubble causes it to shrink.