Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. Find the rise of water in the space between the plates. Surface tension of water `=0.075Nm^-1`.

Explanation

To solve the problem of finding the rise of water between two parallel glass plates, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Involved**:
The rise of water between the plates is due to the surface tension of the water. The upward force due to surface tension must balance the downward weight of the water column that rises between the plates.

2. **Identify the Variables**:
- Surface tension of water, \( S = 0.075 \, \text{N/m} \)
- Separation between the plates, \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)
- Length of the plates in contact with water, \( L = 1 \, \text{m} \) (assuming unit length)

3. **Calculate the Surface Tension Force**:
The total upward force due to surface tension acting on the water is given by:
\[ F_{\text{surface tension}} = 2S \cdot L \]
Here, the factor of 2 accounts for the two surfaces (the two plates).

4. **Calculate the Weight of the Water Column**:
The weight of the water column that rises between the plates can be expressed as:
\[ F_{\text{weight}} = \rho \cdot g \cdot h \cdot A \]
Where \( A \) is the cross-sectional area of the water column. For unit length, \( A = 1 \, \text{m}^2 \), so:
\[ F_{\text{weight}} = \rho \cdot g \cdot h \]

5. **Set the Forces Equal**:
Since the upward force due to surface tension must equal the downward weight of the water:
\[ 2S \cdot L = \rho \cdot g \cdot h \]

6. **Solve for the Rise of Water \( h \)**:
Rearranging the equation gives:
\[ h = \frac{2SL}{\rho g} \]

7. **Substitute the Values**:
Now, substituting the known values into the equation:
\[ h = \frac{2 \cdot 0.075 \cdot 1}{1000 \cdot 10} \]
\[ h = \frac{0.15}{10000} = 0.000015 \, \text{m} \]
Converting this to centimeters:
\[ h = 0.000015 \, \text{m} \times 100 \, \text{cm/m} = 1.5 \, \text{cm} \]

### Final Answer:
The rise of water in the space between the plates is **1.5 cm**.