A drop of water of volume `0.05 cm^(3)` is pressed between two glass plates, as a consequence of which, it spreads and occupies an are of `40 cm^(2)`. If the surface tension of water is `70 "dyne"//cm`, find the normal force required to separate out the two glass plates is newton.

Explanation

To solve the problem, we need to find the normal force required to separate two glass plates with a drop of water in between. The steps are as follows:

### Step 1: Calculate the thickness of the water layer
The volume of the water drop is given as \( V = 0.05 \, \text{cm}^3 \) and the area it occupies is \( A = 40 \, \text{cm}^2 \).

The thickness \( d \) of the water layer can be calculated using the formula:
\[ d = \frac{V}{A} \]
Substituting the values:
\[ d = \frac{0.05 \, \text{cm}^3}{40 \, \text{cm}^2} = \frac{0.05}{40} = 0.00125 \, \text{cm} \]

### Step 2: Convert thickness to meters
To work in standard SI units, convert the thickness from centimeters to meters:
\[ d = 0.00125 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.0000125 \, \text{m} \]

### Step 3: Calculate the length of contact
The length of contact \( L \) can be determined using the area and thickness:
\[ L = \frac{A}{d} \]
Substituting the values:
\[ L = \frac{40 \times 10^{-4} \, \text{m}^2}{0.0000125 \, \text{m}} = \frac{0.004 \, \text{m}^2}{0.0000125 \, \text{m}} = 320 \, \text{m} \]

### Step 4: Calculate the force due to surface tension
The force \( F \) due to surface tension is given by:
\[ F = 2T \cdot L \]
Where \( T \) is the surface tension of water, given as \( 70 \, \text{dyne/cm} \). We need to convert this to SI units (N/m):
\[ T = 70 \, \text{dyne/cm} = 70 \times 10^{-5} \, \text{N/m} \]

Now substituting the values into the force equation:
\[ F = 2 \cdot (70 \times 10^{-5} \, \text{N/m}) \cdot (320 \, \text{m}) \]
Calculating this gives:
\[ F = 2 \cdot 70 \cdot 320 \times 10^{-5} = 44800 \times 10^{-5} \, \text{N} = 4.48 \, \text{N} \]

### Step 5: Final answer
Thus, the normal force required to separate the two glass plates is approximately:
\[ F \approx 4.48 \, \text{N} \]

### Summary of Steps:
1. Calculate the thickness of the water layer using volume and area.
2. Convert the thickness to meters.
3. Calculate the length of contact using area and thickness.
4. Calculate the force due to surface tension.
5. Present the final answer.