The surface tension of a liquid is `5` Newton per metre. If a film is held on a ring of area `0.02 metres^(2)`, its surface energy is about :

Options

A. `5 xx 10^(-2) J`
B. `2.5 xx 10^(-2) J`
C. `2 xx 10^(-1) J`
D. `3 xx 10^(-1) J`

Explanation

To find the surface energy of a liquid film held on a ring, we can follow these steps:

### Step 1: Understand the Concept of Surface Tension
Surface tension (T) is defined as the force per unit length acting on the surface of a liquid. It is measured in Newtons per meter (N/m).

### Step 2: Identify the Given Values
From the problem, we know:
- Surface tension (T) = 5 N/m
- Area (A) = 0.02 m²

### Step 3: Determine the Number of Surfaces
When a film is held on a ring, it creates two surfaces (one on the top and one on the bottom). Therefore, we need to consider both surfaces when calculating the surface energy.

### Step 4: Use the Formula for Surface Energy
The surface energy (E) can be calculated using the formula:
\[ E = T \times A_{\text{total}} \]
Where \( A_{\text{total}} \) is the total area of the surfaces. Since there are two surfaces, we have:
\[ A_{\text{total}} = 2 \times A \]

### Step 5: Substitute the Values into the Formula
Now we can substitute the values into the formula:
\[ A_{\text{total}} = 2 \times 0.02 \, \text{m}^2 = 0.04 \, \text{m}^2 \]
Now, calculate the surface energy:
\[ E = T \times A_{\text{total}} = 5 \, \text{N/m} \times 0.04 \, \text{m}^2 \]

### Step 6: Calculate the Surface Energy
Calculating the above expression gives:
\[ E = 5 \times 0.04 = 0.2 \, \text{J} \]

### Step 7: Final Result
Thus, the surface energy of the film is approximately:
\[ E \approx 0.2 \, \text{J} \]