Two vertical glass plates 1 mm apart are dipped into water. How high will the water rise between the plates. If the surface tension of water is 70 dyne `cm^(-1)`

Options

A. 1.43 cm
B. 1.63 cm
C. 2.86 cm
D. 3.86 cm

Answer

To solve the problem of how high the water will rise between two vertical glass plates that are 1 mm apart, we will use the concept of capillary rise, which is influenced by surface tension.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Distance between the plates (D) = 1 mm = 0.1 cm
- Surface tension of water (T) = 70 dyne/cm
- Density of water (ρ) = 1 g/cm³ (approximately)
- Acceleration due to gravity (g) = 980 cm/s² (in cgs units)

2. **Set Up the Equation for Capillary Rise:**
The height (h) to which the water rises between the plates can be derived from the balance of forces due to surface tension and the weight of the water column. The formula for capillary rise is given by:
\[ h = \frac{2T}{\rho g D} \]
where:
- \( T \) = surface tension,
- \( \rho \) = density of the liquid,
- \( g \) = acceleration due to gravity,
- \( D \) = distance between the plates.

3. **Substitute the Known Values:**
Now, substituting the known values into the formula:
\[ h = \frac{2 \times 70 \, \text{dyne/cm}}{1 \, \text{g/cm}^3 \times 980 \, \text{cm/s}^2 \times 0.1 \, \text{cm}} \]

4. **Calculate the Height:**
- Calculate the numerator:
\[ 2 \times 70 = 140 \, \text{dyne/cm} \]
- Calculate the denominator:
\[ 1 \times 980 \times 0.1 = 98 \, \text{g cm/s}^2 \]
- Now substitute these values into the equation:
\[ h = \frac{140}{98} \, \text{cm} \approx 1.42857 \, \text{cm} \]

5. **Final Result:**
Rounding this to two decimal places, we find:
\[ h \approx 1.43 \, \text{cm} \]

### Conclusion:
The height to which the water will rise between the plates is approximately **1.43 cm**.