Calculate the force required to take away a flat circular plate of radius 0.02m from the surface of water. The surface tension of water is `0.07 Nm^(-1)`

Explanation

To calculate the force required to take away a flat circular plate from the surface of water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the circular plate, \( R = 0.02 \, \text{m} \)
- Surface tension of water, \( \sigma = 0.07 \, \text{N/m} \)

2. **Calculate the Circumference of the Circular Plate:**
- The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi R \]
- Substituting the value of \( R \):
\[ C = 2 \pi (0.02) = 0.04 \pi \, \text{m} \]

3. **Calculate the Force Required:**
- The force \( F \) required to detach the plate from the water surface can be calculated using the formula:
\[ F = C \cdot \sigma \]
- Substituting the values of \( C \) and \( \sigma \):
\[ F = (0.04 \pi) \cdot (0.07) \]
- Now, calculate \( F \):
\[ F = 0.04 \cdot 3.14 \cdot 0.07 \]
\[ F \approx 0.04 \cdot 0.2198 \approx 0.008792 \, \text{N} \]

4. **Convert to Scientific Notation:**
- The force can be expressed in scientific notation:
\[ F \approx 8.79 \times 10^{-3} \, \text{N} \]
- Rounding off gives:
\[ F \approx 8.8 \times 10^{-3} \, \text{N} \]

### Final Answer:
The force required to take away the flat circular plate from the surface of water is approximately \( 8.8 \times 10^{-3} \, \text{N} \).