Find the stress to be applied to a steel wire to stretched it by 0.025% of its original length. Y for steel is 90 GPa.

Explanation

To find the stress to be applied to a steel wire to stretch it by 0.025% of its original length, we can follow these steps:

### Step 1: Understand the given data
- Percentage change in length (strain) = 0.025%
- Young's modulus for steel (Y) = 90 GPa = \(90 \times 10^9 \, \text{Pa}\)

### Step 2: Convert percentage strain to decimal strain
Strain (\(\epsilon\)) is defined as the change in length divided by the original length. It can be expressed as:
\[ \epsilon = \frac{\Delta L}{L} = \frac{0.025}{100} = 0.00025 \]

### Step 3: Use Young's modulus formula
Young's modulus (Y) relates stress (\(\sigma\)) and strain (\(\epsilon\)) as follows:
\[ Y = \frac{\sigma}{\epsilon} \]
From this, we can rearrange the formula to find stress:
\[ \sigma = Y \cdot \epsilon \]

### Step 4: Substitute the values into the formula
Substituting the values of Y and \(\epsilon\) into the equation:
\[ \sigma = 90 \times 10^9 \, \text{Pa} \cdot 0.00025 \]

### Step 5: Calculate the stress
Now, calculate the stress:
\[ \sigma = 90 \times 10^9 \cdot 0.00025 = 22.5 \times 10^6 \, \text{Pa} \]
This can also be expressed in megapascals:
\[ \sigma = 22.5 \, \text{MPa} \]

### Final Answer
The stress required to stretch the steel wire by 0.025% of its original length is **22.5 MPa**.

---