The work done in blowing a soap bubble of radius 5 cm is

Options

A. 750 J
B. 1570 J
C. `1.57 xx10^(2)`erg
D. `1.57 xx 10^(4)`erg

Explanation

To find the work done in blowing a soap bubble of radius 5 cm, we will follow these steps:

### Step 1: Understand the Formula for Work Done
The work done (W) in blowing a soap bubble can be calculated using the formula:
\[ W = \text{Surface Tension} \times \text{Total Surface Area} \]

### Step 2: Calculate the Total Surface Area of the Soap Bubble
A soap bubble has two surfaces (inner and outer). The surface area (A) of a sphere is given by:
\[ A = 4\pi r^2 \]
Thus, the total surface area (A_total) for the soap bubble is:
\[ A_{\text{total}} = 2 \times A = 2 \times 4\pi r^2 = 8\pi r^2 \]

### Step 3: Substitute the Radius
Given that the radius \( r = 5 \) cm, we can substitute this value into the total surface area formula:
\[ A_{\text{total}} = 8\pi (5 \, \text{cm})^2 \]
\[ A_{\text{total}} = 8\pi (25 \, \text{cm}^2) \]
\[ A_{\text{total}} = 200\pi \, \text{cm}^2 \]

### Step 4: Convert Surface Tension to Appropriate Units
The surface tension is given as \( 25 \, \text{dyn/cm} \). We will use this value directly in our calculations since it is already in CGS units.

### Step 5: Calculate Work Done
Now we can calculate the work done:
\[ W = \text{Surface Tension} \times \text{Total Surface Area} \]
\[ W = 25 \, \text{dyn/cm} \times 200\pi \, \text{cm}^2 \]
\[ W = 5000\pi \, \text{dyn} \cdot \text{cm} \]

### Step 6: Convert to Ergs
Since \( 1 \, \text{dyn} \cdot \text{cm} = 1 \, \text{erg} \), we have:
\[ W = 5000\pi \, \text{ergs} \]
Now, substituting \( \pi \approx 3.14 \):
\[ W \approx 5000 \times 3.14 \]
\[ W \approx 15700 \, \text{ergs} \]

### Final Answer
Thus, the work done in blowing the soap bubble of radius 5 cm is approximately:
\[ W \approx 15700 \, \text{ergs} \]

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