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 find the minimum additional force needed to lift a needle floating on the surface of water, we will use the concept of surface tension. Here are the steps to solve the problem:

### Step 1: Understand the Given Information
- Length of the needle (L) = 2.5 cm = 2.5 × 10^(-2) m
- Surface tension of water (σ) = 0.072 N/m

### Step 2: Calculate the Force Due to Surface Tension
The force due to surface tension (F_t) acting on the needle can be calculated using the formula:
\[ F_t = \sigma \times L_{contact} \]
where \( L_{contact} \) is the length of the needle in contact with the water surface. Since the needle is floating horizontally, the entire length of the needle is in contact with the water.

### Step 3: Determine the Length in Contact with Water
Since the needle is floating, the length in contact with the water is equal to the length of the needle:
\[ L_{contact} = L = 2.5 \times 10^{-2} \, \text{m} \]

### Step 4: Substitute the Values into the Formula
Now, substituting the values into the formula for force due to surface tension:
\[ F_t = \sigma \times L_{contact} = 0.072 \, \text{N/m} \times 2.5 \times 10^{-2} \, \text{m} \]

### Step 5: Perform the Calculation
Calculating the force:
\[ F_t = 0.072 \times 2.5 \times 10^{-2} \]
\[ F_t = 0.072 \times 0.025 \]
\[ F_t = 0.0018 \, \text{N} \]

### Step 6: Convert to Millinewtons
To express this in millinewtons:
\[ F_t = 1.8 \, \text{mN} \]

### Step 7: Conclusion
The minimum additional force needed to lift the needle above the surface of the water is:
\[ F_{additional} = F_t = 1.8 \, \text{mN} \]

### Final Answer
The minimum force in addition to its weight needed to lift the needle above the surface of water is \( 1.8 \, \text{mN} \).

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