Select the incorrect option (T = surface tension, R = radius of drop, bubble, meniscus)

Options

A. Excess pressure inside a liquid drop in air is equal to `(2T)/(R)`
B. Excess presure inside a liquid bubbles in air is equal to `(2T)/(R)`
C. Excess pressure for spherical liquid meniscus is `(4T)/(R)`
D. Excess pressure for cylindrical bubble in air is `(4T)/(R)`

Answer

To solve the problem of selecting the incorrect option regarding the excess pressure in different fluid situations, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Surface Tension and Excess Pressure**:
- Surface tension (T) is a property of the liquid that causes it to behave like a stretched elastic membrane.
- Excess pressure (ΔP) across a curved surface is related to surface tension and the radius of curvature.

2. **Analyzing Option 1**:
- **Statement**: Excess pressure inside a liquid drop in air is equal to \( \frac{2T}{R} \).
- **Analysis**: A liquid drop in air has one curved surface. The formula for excess pressure for a drop is indeed \( \Delta P = \frac{2T}{R} \).
- **Conclusion**: Option 1 is **correct**.

3. **Analyzing Option 2**:
- **Statement**: Excess pressure inside a liquid bubble in air is equal to \( \frac{2T}{R} \).
- **Analysis**: A liquid bubble has two surfaces (inner and outer). The correct formula for excess pressure in a bubble is \( \Delta P = \frac{4T}{R} \) (since there are two surfaces contributing to the pressure).
- **Conclusion**: Option 2 is **incorrect**.

4. **Analyzing Option 3**:
- **Statement**: Excess pressure of a spherical liquid meniscus is \( \frac{4T}{R} \).
- **Analysis**: A spherical meniscus has only one surface, so the correct excess pressure is \( \Delta P = \frac{2T}{R} \).
- **Conclusion**: Option 3 is **incorrect**.

5. **Analyzing Option 4**:
- **Statement**: Excess pressure for a cylindrical bubble in air is \( \frac{4T}{R} \).
- **Analysis**: A cylindrical bubble has two surfaces, so the correct excess pressure is \( \Delta P = \frac{2T}{R} \).
- **Conclusion**: Option 4 is **incorrect**.

### Final Conclusion:
The incorrect options are **2, 3, and 4**.