Which of the following is correct ?

Options

A. The excess pressure inside a spherical drop of liquid is 2T/R
B. The excess pressure inside a spherical soap bubble is 4T/R
C. The excess pressure inside a cylindrical drop of liquid is T/R
D. Only (A) and (B)

Answer

To solve the problem regarding excess pressure in different types of drops, we will analyze each case step by step.

### Step 1: Excess Pressure in a Spherical Drop
- For a spherical drop, the excess pressure (\( \Delta P \)) inside the drop can be derived from the balance of forces due to surface tension.
- The formula for excess pressure inside a spherical drop is given by:
\[ \Delta P = \frac{2T}{R} \]
where \( T \) is the surface tension and \( R \) is the radius of the drop.

### Step 2: Excess Pressure in a Spherical Soap Bubble
- A soap bubble has two surfaces (inner and outer). Therefore, the excess pressure inside a soap bubble is given by:
\[ \Delta P = \frac{4T}{R} \]
This is because the surface tension acts on both surfaces of the bubble.

### Step 3: Excess Pressure in a Cylindrical Drop
- For a cylindrical drop, we need to consider the geometry of the cylinder. The excess pressure can be derived by analyzing the forces acting on the curved surface of the cylinder.
- The formula for excess pressure inside a cylindrical drop is:
\[ \Delta P = \frac{T}{R} \]
However, since the height of the cylinder also plays a role, the correct expression should include the height, leading to:
\[ \Delta P = \frac{T}{R} + \text{(additional terms depending on height)} \]
This indicates that the excess pressure is not simply \( \frac{T}{R} \).

### Conclusion
- Based on the analysis:
- Excess pressure inside a spherical drop: \( \Delta P = \frac{2T}{R} \) (Correct)
- Excess pressure inside a spherical soap bubble: \( \Delta P = \frac{4T}{R} \) (Correct)
- Excess pressure inside a cylindrical drop: Not simply \( \frac{T}{R} \) (Incorrect)

Thus, the correct options are A and B.

### Final Answer
The correct options are A and B.

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