Two glass plates are separated by water. If surface tension of water is `75 dyn//cm` and the area of each plate wetted by water is `8 cm^(2)` and the distance between the plates is `0.12 mm`, then the force applied to separate the two plates is

Options

A. `10^(2)dyn`
B. `10^(4)dyn`
C. `10^(5)dyn`
D. `10^(6)dyn`

Explanation

To find the force required to separate the two glass plates that are in contact with water, we can follow these steps:

### Step 1: Understand the Given Data
- Surface tension of water, \( \sigma = 75 \, \text{dyn/cm} \)
- Area of each plate wetted by water, \( A = 8 \, \text{cm}^2 \)
- Distance between the plates, \( d = 0.12 \, \text{mm} = 0.012 \, \text{cm} \)

### Step 2: Calculate the Total Length in Contact
The total length in contact, \( L \), can be calculated using the formula:
\[ L = \frac{A}{d} \]
Substituting the values:
\[ L = \frac{8 \, \text{cm}^2}{0.012 \, \text{cm}} = \frac{8}{0.012} \, \text{cm} = 666.67 \, \text{cm} \]

### Step 3: Calculate the Force Due to Surface Tension
The force due to surface tension can be calculated using the formula:
\[ F = \sigma \times L \]
Since there are two plates, the total force will be:
\[ F_{\text{total}} = 2 \times \sigma \times L \]
Substituting the values:
\[ F_{\text{total}} = 2 \times 75 \, \text{dyn/cm} \times 666.67 \, \text{cm} \]
Calculating this gives:
\[ F_{\text{total}} = 2 \times 75 \times 666.67 = 10000 \, \text{dyn} \]

### Step 4: Final Result
The force applied to separate the two plates is:
\[ F_{\text{total}} = 10^5 \, \text{dyn} \]

### Summary
Thus, the force required to separate the two glass plates is \( 10^5 \, \text{dyn} \).

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