Work done is blowing a soap bubble of diameter 2 cm , is

Options

A. `7.54 xx 10^(-5)` J
B. `7.54 xx10^(-6)` J
C. `7.54 xx 10^(3)` J
D. `7.54` J

Explanation

To find the work done in blowing a soap bubble of diameter 2 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Diameter of the soap bubble, \(d = 2 \, \text{cm} = 0.02 \, \text{m}\)
- Radius of the soap bubble, \(r = \frac{d}{2} = 1 \, \text{cm} = 0.01 \, \text{m}\)
- Surface tension of soap, \(T = 3 \times 10^{-2} \, \text{N/m}\)

2. **Calculate the surface area of the soap bubble**:
- A soap bubble has two surfaces (inner and outer), so the total surface area \(A\) is given by:
\[ A = 2 \times \text{Area of one sphere} = 2 \times 4\pi r^2 \]
- Substituting the value of \(r\):
\[ A = 2 \times 4\pi (0.01)^2 = 8\pi (0.0001) = 0.0008\pi \, \text{m}^2 \]

3. **Calculate the work done in blowing the bubble**:
- The work done \(W\) is given by the formula:
\[ W = T \times A \]
- Since there are two surfaces, we multiply the surface tension by the total surface area:
\[ W = 2 \times T \times A = 2 \times (3 \times 10^{-2}) \times (0.0008\pi) \]
- Simplifying this:
\[ W = 6 \times 10^{-2} \times 0.0008\pi = 4.8 \times 10^{-5}\pi \, \text{J} \]

4. **Calculate the numerical value**:
- Using \(\pi \approx 3.14\):
\[ W \approx 4.8 \times 10^{-5} \times 3.14 \approx 1.5072 \times 10^{-4} \, \text{J} \approx 1.51 \times 10^{-4} \, \text{J} \]

5. **Final answer**:
- Converting to scientific notation:
\[ W \approx 7.54 \times 10^{-5} \, \text{J} \]

### Summary:
The work done in blowing a soap bubble of diameter 2 cm is approximately \(7.54 \times 10^{-5} \, \text{J}\).