The surface tension soap solution is ` 3 xx 10^(-2)` N/m then then the work done in forming a soap film of ` 20 cm xx 5 ` cm will be

Explanation

To solve the problem, we need to calculate the work done in forming a soap film with given dimensions and surface tension. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Surface tension of the soap solution (T) = \(3 \times 10^{-2}\) N/m
- Dimensions of the soap film:
- Length (l) = 20 cm = 0.2 m
- Width (w) = 5 cm = 0.05 m

### Step 2: Calculate the area of the soap film
The area (A) of the soap film can be calculated using the formula:
\[ A = l \times w \]
Substituting the values:
\[ A = 0.2 \, \text{m} \times 0.05 \, \text{m} = 0.01 \, \text{m}^2 \]

### Step 3: Determine the total surface area of the soap film
Since a soap film has two surfaces, the total surface area (ΔA) is:
\[ \Delta A = 2 \times A = 2 \times 0.01 \, \text{m}^2 = 0.02 \, \text{m}^2 \]

### Step 4: Calculate the work done (W)
The work done in forming the soap film can be calculated using the formula:
\[ W = T \times \Delta A \]
Substituting the values:
\[ W = (3 \times 10^{-2} \, \text{N/m}) \times (0.02 \, \text{m}^2) \]
\[ W = 6 \times 10^{-4} \, \text{N m} \]

### Final Answer
The work done in forming the soap film is \(6 \times 10^{-4}\) N m.

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