The surface tension of soap water is 0.04 N/m. The excess pressure inside a 10 mm diameter soap bubble in will be

Options

A. 4
B. 8
C. 16
D. 32

Explanation

To solve the problem of finding the excess pressure inside a soap bubble, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Surface tension (T) = 0.04 N/m
- Diameter of the soap bubble = 10 mm

2. **Calculate the Radius:**
- The radius (R) is half of the diameter.
\[ R = \frac{\text{Diameter}}{2} = \frac{10 \text{ mm}}{2} = 5 \text{ mm} \]
- Convert the radius from mm to meters:
\[ R = 5 \text{ mm} = 5 \times 10^{-3} \text{ m} \]

3. **Use the Formula for Excess Pressure:**
- The formula for excess pressure (P) inside a soap bubble is given by:
\[ P = \frac{4T}{R} \]
- Substitute the values of T and R into the formula:
\[ P = \frac{4 \times 0.04 \text{ N/m}}{5 \times 10^{-3} \text{ m}} \]

4. **Calculate the Excess Pressure:**
- Perform the calculation:
\[ P = \frac{0.16 \text{ N/m}}{5 \times 10^{-3} \text{ m}} = 0.16 \div 0.005 = 32 \text{ N/m}^2 \]

5. **Conclusion:**
- The excess pressure inside the soap bubble is:
\[ P = 32 \text{ N/m}^2 \]

### Final Answer:
The excess pressure inside the soap bubble is **32 N/m²**.

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