The surface tension of soap solution is `0.03 N//m` . The work done in blowing to from a soap bublle of surface area `40 cm^(2)`, (in J) , is

Options

A. `2.4xx10^(-4)` J
B. `1.2xx10^(-2)` J
C. `3.6xx10^(-4)` J
D. `4.2xx10^(-2)` J

Explanation

To solve the problem of calculating the work done in blowing a soap bubble with a given surface area and surface tension, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Surface tension (T) = 0.03 N/m
- Surface area (A) = 40 cm² = 40 × 10⁻⁴ m² (since 1 cm² = 10⁻⁴ m²)

2. **Calculate the Change in Surface Area:**
- When blowing a soap bubble, the change in surface area (ΔA) is given by the formula:
\[ \Delta A = 2A \]
- Here, A is the surface area of the bubble. Therefore:
\[ \Delta A = 2 \times (40 \times 10^{-4}) = 80 \times 10^{-4} \text{ m}^2 \]

3. **Calculate the Work Done:**
- The work done (W) in blowing the bubble can be calculated using the formula:
\[ W = \Delta A \times T \]
- Substituting the values we have:
\[ W = (80 \times 10^{-4}) \times 0.03 \]
- Simplifying this:
\[ W = 80 \times 0.03 \times 10^{-4} = 2.4 \times 10^{-4} \text{ J} \]

4. **Final Result:**
- The work done in blowing the soap bubble is:
\[ W = 2.4 \times 10^{-4} \text{ J} \]

### Summary:
The work done in blowing a soap bubble of surface area 40 cm² with a surface tension of 0.03 N/m is **2.4 × 10⁻⁴ J**.