The soap bubble formed at the end of the tube is blown very slowly. Draw the graph between excess of pressure inside the bubble with time.

Options

A.
B.
C.
D.

Explanation

To solve the problem of drawing the graph between the excess pressure inside a soap bubble and time as the bubble is blown slowly, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Excess Pressure in a Soap Bubble**:
- The excess pressure \( P \) inside a soap bubble of radius \( r \) is given by the formula:
\[ P = \frac{4S}{r} \]
where \( S \) is the surface tension of the soap solution.

2. **Behavior of the Bubble**:
- When a soap bubble is blown slowly, the radius \( r \) of the bubble increases over time. As the radius increases, we can analyze how the excess pressure changes.

3. **Relationship Between Pressure and Radius**:
- From the formula, we can see that the excess pressure \( P \) is inversely proportional to the radius \( r \):
\[ P \propto \frac{1}{r} \]
- This means that as the radius \( r \) increases, the excess pressure \( P \) decreases.

4. **Graphical Representation**:
- Since \( P \) decreases as \( r \) increases, we can represent this relationship graphically.
- The graph of excess pressure \( P \) versus time \( t \) will show a decreasing trend. As time progresses and the bubble expands, the pressure will drop.

5. **Shape of the Graph**:
- The relationship is not linear; instead, it can be represented as a parabolic curve that approaches the time axis as time increases, indicating that the pressure approaches zero as the bubble continues to expand indefinitely.

6. **Identifying the Correct Graph**:
- Upon reviewing the options provided, the graph that shows a parabolic decrease of pressure over time is the correct one.

### Conclusion:
The graph of excess pressure inside the soap bubble versus time will be a downward-opening parabola, reflecting the inverse relationship between pressure and radius as the bubble expands.