A small drop of water of surface tension ` sigma ` is squeezed between two clean glass plates so that a thin layer of thickness d and area A is formed between them. If the angle of contact is zero, what is the force required to pull the plates apart?

Options

A. ` (sigma A )/ (d ) `
B. ` (2 sigma A )/( d ) `
C. ` (4 sigma A )/(d) `
D. ` (8 sigma A )/(d) `

Explanation

To find the force required to pull the two glass plates apart when a thin layer of water is squeezed between them, we can follow these steps:

### Step 1: Understand the Problem
We have a thin layer of water with thickness \( d \) and area \( A \) between two glass plates. The surface tension of the water is denoted by \( \sigma \), and the angle of contact is zero.

### Step 2: Determine the Length in Contact
The length of the water film in contact with the plates can be determined from the area \( A \) and thickness \( d \). Since the area \( A \) is given by:
\[ A = \text{length} \times \text{width} \]
and the width is equal to the thickness \( d \), we can express the length \( L \) in contact as:
\[ L = \frac{A}{d} \]

### Step 3: Calculate the Total Length in Contact
Since there are two surfaces (top and bottom) in contact with the water film, the total length in contact is:
\[ \text{Total Length} = 2L = 2 \times \frac{A}{d} = \frac{2A}{d} \]

### Step 4: Calculate the Force Due to Surface Tension
The force \( F \) required to separate the plates is related to the surface tension and the total length in contact. The force due to surface tension is given by:
\[ F = \sigma \times \text{Total Length} \]
Substituting the total length we found in the previous step:
\[ F = \sigma \times \frac{2A}{d} \]

### Final Answer
Thus, the force required to pull the plates apart is:
\[ F = \frac{2\sigma A}{d} \]