The work done in blowing a soap bubble of 10 cm radius is (Surface tension of the soap solution is `3/100` N/m)

Options

A. `75.36xx10^(-4) ` joule
B. `37.68xx10^(-4) ` joule
C. `150.72xx10^(-4)` joule
D. 75.36 joule

Answer

To find the work done in blowing a soap bubble, we can use the formula:

\[ W = \Delta A \cdot \gamma \]

where:
- \( W \) is the work done,
- \( \Delta A \) is the change in surface area,
- \( \gamma \) is the surface tension of the soap solution.

### Step 1: Calculate the surface area of the soap bubble
The surface area \( A \) of a sphere is given by the formula:

\[ A = 4 \pi r^2 \]

where \( r \) is the radius of the bubble. Given that the radius \( r = 10 \) cm = 0.1 m, we can calculate the surface area.

### Calculation:
\[ A = 4 \pi (0.1)^2 \]
\[ A = 4 \pi (0.01) \]
\[ A = 0.04 \pi \, \text{m}^2 \]

### Step 2: Determine the change in surface area
When blowing a soap bubble, we need to consider that a soap bubble has two surfaces (inner and outer). Therefore, the total surface area of the bubble is:

\[ A_{\text{total}} = 2 \times A \]
\[ A_{\text{total}} = 2 \times 0.04 \pi \]
\[ A_{\text{total}} = 0.08 \pi \, \text{m}^2 \]

### Step 3: Calculate the work done
Now we can substitute the values into the work done formula. The surface tension \( \gamma = \frac{3}{100} \, \text{N/m} = 0.03 \, \text{N/m} \).

### Calculation:
\[ W = \Delta A \cdot \gamma \]
\[ W = 0.08 \pi \cdot 0.03 \]
\[ W = 0.0024 \pi \, \text{J} \]

### Step 4: Final result
To get a numerical value, we can approximate \( \pi \approx 3.14 \):

\[ W \approx 0.0024 \times 3.14 \]
\[ W \approx 0.00754 \, \text{J} \]

Thus, the work done in blowing the soap bubble is approximately \( 0.00754 \, \text{J} \).

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