The length of a needle floating on water is `2.5 cm`. The minimum force in addition to its weight needed to lift the needle above the surface of water will be (surface tension of water is `0.072 N//m`)

Options

A. `3.6xx10^(-3)N`
B. `10^(-2)N`
C. `9xx10^(-4)N`
D. `6xx10^(-4)N`

Explanation

To solve the problem, we need to calculate the minimum force required to lift a needle floating on the surface of water, taking into account the surface tension of the water.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length of the needle, \( L = 2.5 \, \text{cm} = 2.5 \times 10^{-2} \, \text{m} \)
- Surface tension of water, \( \gamma = 0.072 \, \text{N/m} \)

2. **Understand the Concept of Surface Tension:**
- Surface tension creates a force that acts along the surface of the liquid. For a floating object like a needle, the surface tension acts at the edges of the needle.

3. **Calculate the Force Due to Surface Tension:**
- The total force due to surface tension acting on the needle can be calculated using the formula:
\[ F = \gamma \times 2L \]
- Here, \( 2L \) accounts for the two edges of the needle that are in contact with the water surface.

4. **Substitute the Values:**
- Substitute the values into the formula:
\[ F = 0.072 \, \text{N/m} \times 2 \times (2.5 \times 10^{-2} \, \text{m}) \]

5. **Perform the Calculation:**
- Calculate \( 2L \):
\[ 2L = 2 \times 2.5 \times 10^{-2} = 5.0 \times 10^{-2} \, \text{m} \]
- Now calculate the force:
\[ F = 0.072 \times 5.0 \times 10^{-2} = 0.072 \times 0.05 = 0.0036 \, \text{N} \]
- Convert this to scientific notation:
\[ F = 3.6 \times 10^{-3} \, \text{N} \]

6. **Conclusion:**
- The minimum force in addition to the weight needed to lift the needle above the surface of the water is \( 3.6 \times 10^{-3} \, \text{N} \).

### Final Answer:
The minimum force required to lift the needle above the surface of the water is \( 3.6 \times 10^{-3} \, \text{N} \).