A soap bubble of diameter 6mm is formed in air . The surface tension of liquid is 30 dyne/cm . The excess pressure inside the soap bubble is

Options

A. 150 dyne`//cm^2`
B. 300 dyne`//cm^2`
C. 400 dyne`//cm^2`
D. `3xx10^(-3)` dyne`//cm^2`

Answer

To solve the problem of finding the excess pressure inside a soap bubble, we will follow these steps:

### Step 1: Understand the formula for excess pressure in a soap bubble
The excess pressure (ΔP) inside a soap bubble is given by the formula:
\[ \Delta P = \frac{4T}{R} \]
where:
- \( T \) is the surface tension of the liquid,
- \( R \) is the radius of the soap bubble.

### Step 2: Identify the given values
From the problem statement, we have:
- Diameter of the soap bubble = 6 mm
- Surface tension \( T = 30 \) dyne/cm

### Step 3: Calculate the radius of the soap bubble
The radius \( R \) is half of the diameter:
\[ R = \frac{\text{Diameter}}{2} = \frac{6 \text{ mm}}{2} = 3 \text{ mm} \]

### Step 4: Convert the radius to centimeters
Since the surface tension is given in dyne/cm, we need to convert the radius from mm to cm:
\[ R = 3 \text{ mm} = 0.3 \text{ cm} \]

### Step 5: Substitute the values into the formula
Now we can substitute the values of \( T \) and \( R \) into the formula for excess pressure:
\[ \Delta P = \frac{4 \times 30 \text{ dyne/cm}}{0.3 \text{ cm}} \]

### Step 6: Perform the calculation
Calculating the excess pressure:
\[ \Delta P = \frac{120 \text{ dyne/cm}}{0.3 \text{ cm}} = 400 \text{ dyne/cm}^2 \]

### Step 7: State the final answer
The excess pressure inside the soap bubble is:
\[ \Delta P = 400 \text{ dyne/cm}^2 \]

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