The length of needle foating on the surface of water is 1.5 cm the force in addition to its weight required to lift the needle from water surface will be (surface tension of water `=7.5N//cm`)

Options

A. 22.5 N
B. 2.25 N
C. 0.25 N
D. 225 N

Answer

To solve the problem of finding the force in addition to the weight required to lift a needle floating on the surface of water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length of the needle (L) = 1.5 cm
- Surface tension of water (T) = 7.5 N/cm

2. **Understand the Concept of Surface Tension:**
- Surface tension acts along the length of the needle and is present on both sides of the needle. Therefore, the effective length that contributes to the surface tension is twice the length of the needle.

3. **Calculate the Effective Length:**
- Effective length = 2 × L
- Effective length = 2 × 1.5 cm = 3 cm

4. **Calculate the Force Due to Surface Tension:**
- The force (F) required to lift the needle from the water surface can be calculated using the formula:
\[ F = T \times \text{Effective Length} \]
- Substitute the values:
\[ F = 7.5 \, \text{N/cm} \times 3 \, \text{cm} \]
- Calculate the force:
\[ F = 22.5 \, \text{N} \]

5. **Conclusion:**
- The force in addition to the weight required to lift the needle from the water surface is **22.5 N**.

### Final Answer:
The force required to lift the needle from the water surface is **22.5 N**.

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