Assertion : To increase the length of a thin steel wire of `0.1 cm^(2)` corss sectional area by `0.1%`, a force of 2000 N is required, its `Y= 200 xx 10^(9) N m ^(-2)`.
Reson : It is calculated by `Y = (F//L)/(Axx DeltaL)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Information
We have a thin steel wire with:
- Cross-sectional area \( A = 0.1 \, \text{cm}^2 = 0.1 \times 10^{-4} \, \text{m}^2 \) (converting cm² to m²)
- Young's modulus \( Y = 200 \times 10^9 \, \text{N/m}^2 \)
- Change in length \( \Delta L \) is \( 0.1\% \) of the original length \( L \).

### Step 2: Express Change in Length
The change in length \( \Delta L \) can be expressed in terms of the original length \( L \):
\[ \frac{\Delta L}{L} = 0.1\% = \frac{0.1}{100} = 0.001 \]
Thus, \( \Delta L = 0.001L \).

### Step 3: Use the Formula for Young's Modulus
The formula for Young's modulus is given by:
\[ Y = \frac{F}{A \cdot \frac{\Delta L}{L}} \]
Rearranging this formula to find the force \( F \):
\[ F = Y \cdot A \cdot \frac{\Delta L}{L} \]

### Step 4: Substitute the Values
Substituting the values into the equation:
\[ F = (200 \times 10^9) \cdot (0.1 \times 10^{-4}) \cdot (0.001) \]

### Step 5: Calculate the Force
Calculating the force step-by-step:
1. Calculate \( A \cdot \Delta L \):
\[ A \cdot \Delta L = (0.1 \times 10^{-4}) \cdot (0.001) = 0.1 \times 10^{-7} = 1 \times 10^{-8} \, \text{m}^2 \]
2. Now substitute back into the force equation:
\[ F = 200 \times 10^9 \cdot 1 \times 10^{-8} \]
\[ F = 2000 \, \text{N} \]

### Step 6: Conclusion
The force required to increase the length of the wire by \( 0.1\% \) is indeed \( 2000 \, \text{N} \). Therefore, the assertion is correct.