A tube of insufficient length is immersed in water (surface tension`=0.7N//m`) with 1 cm of it Given, radius of tube`=1mm`.

Explanation

To solve the problem, we need to find the height to which water rises in a tube due to surface tension. The formula we will use relates the surface tension, the radius of the tube, and the height of the liquid column.

### Step-by-Step Solution

1. **Identify Given Values**:
- Surface tension (T) = 0.7 N/m
- Radius of the tube (r) = 1 mm = 0.001 m (convert to meters for calculations)
- Density of water (ρ) = 1000 kg/m³ (standard value)
- Acceleration due to gravity (g) = 9.81 m/s² (standard value)

2. **Use the Formula for Height of Liquid Column**:
The height (h) to which the liquid rises in the tube due to surface tension can be calculated using the formula:
\[ h = \frac{2T}{\rho g r} \]

3. **Substitute the Values into the Formula**:
\[ h = \frac{2 \times 0.7 \, \text{N/m}}{1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 0.001 \, \text{m}} \]

4. **Calculate the Denominator**:
\[ \rho g r = 1000 \times 9.81 \times 0.001 = 9.81 \, \text{kg/(m}^2\text{s}^2\text{)} \]

5. **Calculate the Height**:
\[ h = \frac{1.4}{9.81} \approx 0.142 \, \text{m} \]

6. **Convert Height to Centimeters**:
\[ h \approx 0.142 \, \text{m} \times 100 \approx 14.2 \, \text{cm} \]

### Final Answer:
The height to which water rises in the tube is approximately **14.2 cm**.