The lower end of a clean glass capillary tube of internal radius `2 xx 10^(-4) m` is dippled into a beaker containing water . The water rise up the tube to a vertical height of `7 xx 10^(-2) m` above its level in the beaker. Calculate the surface tension of water. Density of water = `1000 kg m^(-3), g = 10 m s^(-2)` .

Answer

To calculate the surface tension of water using the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Internal radius of the capillary tube, \( r = 2 \times 10^{-4} \, \text{m} \)
- Height of water rise in the tube, \( h = 7 \times 10^{-2} \, \text{m} \)
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Use the Formula for Surface Tension:**
The formula relating surface tension \( T \), density \( \rho \), gravitational acceleration \( g \), height \( h \), and radius \( r \) is given by:
\[ T = \frac{\rho g h r}{2} \]

3. **Substitute the Values into the Formula:**
Substitute the known values into the formula:
\[ T = \frac{(1000 \, \text{kg/m}^3)(10 \, \text{m/s}^2)(7 \times 10^{-2} \, \text{m})(2 \times 10^{-4} \, \text{m})}{2} \]

4. **Calculate the Numerator:**
First, calculate the product in the numerator:
\[ 1000 \times 10 \times 7 \times 10^{-2} \times 2 = 140000 \times 10^{-2} = 1400 \]

5. **Divide by 2:**
Now, divide the result by 2:
\[ T = \frac{1400}{2} = 700 \, \text{N/m} \]

6. **Final Result:**
Therefore, the surface tension \( T \) of water is:
\[ T = 7 \times 10^{-2} \, \text{N/m} \]

### Summary:
The surface tension of water is \( 7 \times 10^{-2} \, \text{N/m} \).