Question

Two soap bubbles have different radii but their surface tension is same. Mark the correct answer:-
A. Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble.
B. Pressure of the larger bubble is higher than the smaller bubble
C. Both bubbles have the same internal pressure
D. None of the above

Answer 1

Hint: We are given the two bubbles of different radii and the same surface tension. With the help of the formula of pressure inside a bubble $\Delta P=\dfrac{4T}{R}$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
$\Delta P=\dfrac{4T}{R}$
Where R is the radius of the bubble and T is the surface tension.

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
$\Delta P=\dfrac{4T}{R}$

As the surface tension is the same. 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 , then the larger bubble tries to increase its size by decreasing the pressure. Therefore, the air will flow from the smaller bubble to the larger bubble and the size of the larger bubble increases. Hence the internal pressure of the smaller bubble is larger than that of the pressure inside the larger bubble.

Thus, option A is the correct answer.

Note: Remember that when two bubbles are in communication with each other, the air goes from smaller to larger bubbles. Hence the smaller goes on shrinking and the larger one will expand till the smaller bubble reduces.