`A` drop of water of volume `V` is pressed between the two glass plates so as to spread to an area. `A`. If `T` is the surface tension, the normal force required to separate the glass plates is

Options

A. `(TA^(2))/(V)`
B. `(2TA^(2))/(V)`
C. `(4TA^(2))/(V)`
D. `(TA^(2))/(2V)`

Explanation

To solve the problem of finding the normal force required to separate two glass plates with a drop of water between them, we can follow these steps:

### Step 1: Understand the Problem
We have a drop of water with volume \( V \) that is spread between two glass plates over an area \( A \). The surface tension of the water is given as \( T \). We need to find the normal force \( F \) required to separate the glass plates.

### Step 2: Relate Volume and Area
The volume \( V \) of the water drop can be expressed in terms of the height \( h \) of the water film between the plates and the area \( A \):
\[ V = A \cdot h \]
From this, we can express the height \( h \) as:
\[ h = \frac{V}{A} \]

### Step 3: Calculate the Force Due to Surface Tension
The force due to surface tension acts along the edges of the water film. The total force \( F_T \) due to surface tension can be calculated as:
\[ F_T = \text{(length of the edge)} \times T \]
Since there are two surfaces (top and bottom) in contact with the water, the effective length is \( 2A \) (the perimeter of the area \( A \)):
\[ F_T = 2A \cdot T \]

### Step 4: Relate Surface Tension Force to Normal Force
The normal force \( F \) required to separate the plates must balance the force due to surface tension. Therefore, we can equate the normal force to the force due to surface tension:
\[ F = F_T = 2A \cdot T \]

### Final Answer
Thus, the normal force required to separate the glass plates is:
\[ F = 2A \cdot T \]

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