Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement

Options

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

Explanation

To solve the question regarding the internal pressures of two soap bubbles with different radii but the same surface tension, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Excess Pressure in Soap Bubbles**:
The excess pressure inside a soap bubble is given by the formula:
\[ \Delta P = \frac{4S}{R} \]
where \( \Delta P \) is the excess pressure, \( S \) is the surface tension, and \( R \) is the radius of the bubble.

2. **Identify Given Information**:
- Two soap bubbles have different radii: let’s denote the radius of the smaller bubble as \( R_2 \) and the radius of the larger bubble as \( R_1 \) (where \( R_1 > R_2 \)).
- The surface tension \( S \) is the same for both bubbles.

3. **Apply the Formula for Each Bubble**:
- For the smaller bubble (radius \( R_2 \)):
\[ \Delta P_2 = \frac{4S}{R_2} \]
- For the larger bubble (radius \( R_1 \)):
\[ \Delta P_1 = \frac{4S}{R_1} \]

4. **Analyze the Relationship**:
Since \( R_2 < R_1 \), it follows that:
\[ \Delta P_2 = \frac{4S}{R_2} > \Delta P_1 = \frac{4S}{R_1} \]
This indicates that the excess pressure (or internal pressure) of the smaller bubble is greater than that of the larger bubble.

5. **Conclusion**:
Therefore, the correct statement is:
- The internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble.

### Final Answer:
The correct statement is **Option A**: The internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble.

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