Two unequal soap bubbles are formed one on each side of a tube closed in the middle by a tap. What happens when the tap is opened to put the two bubbles in communication?

Options

A. No air passes in any direction as the pressures are the same on two sides of the tap
B. Larger bubble shrinks and smaller bubble increases in size till they bexome equal in size
C. Smaller bubble gradually collapses and the bigger one increases in size
D. None of the above

Explanation

To solve the problem of what happens when two unequal soap bubbles are connected by a tube after the tap is opened, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Bubbles**:
- Let's denote the smaller bubble as Bubble 1 with radius \( r_1 \) and the larger bubble as Bubble 2 with radius \( r_2 \).
- We know that \( r_1 < r_2 \).

2. **Understand the Pressure Inside the Bubbles**:
- The pressure inside a soap bubble can be described by the formula:
\[ P = P_0 + \frac{4T}{R} \]
where \( P_0 \) is the atmospheric pressure, \( T \) is the surface tension of the soap solution, and \( R \) is the radius of the bubble.

3. **Calculate the Pressures**:
- For the smaller bubble (Bubble 1):
\[ P_1 = P_0 + \frac{4T}{r_1} \]
- For the larger bubble (Bubble 2):
\[ P_2 = P_0 + \frac{4T}{r_2} \]

4. **Compare the Pressures**:
- Since \( r_1 < r_2 \), it follows that \( \frac{4T}{r_1} > \frac{4T}{r_2} \).
- Therefore, we can conclude that:
\[ P_1 > P_2 \]

5. **Determine the Flow of Air**:
- Because the pressure in the smaller bubble (Bubble 1) is greater than that in the larger bubble (Bubble 2), when the tap is opened, air will flow from the smaller bubble to the larger bubble.

6. **Result of the Flow**:
- As air flows from Bubble 1 to Bubble 2, the smaller bubble will gradually collapse, while the larger bubble will increase in size.

7. **Conclusion**:
- Thus, when the tap is opened, the smaller bubble collapses, and the larger bubble expands.

### Final Answer:
When the tap is opened, the smaller bubble collapses, and the larger bubble expands.

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