If the stress on a wire is 10$^{7}$NM$^{-2}$ and the wire is stretched from its original length of 10.00m to 10.05m. The young's modulus of the wire is?

1. Analyze the question

We are given:

• Stress ($\sigma$): $10^7 \, \text{Nm}^{-2}$
• Original length ($L$): $10.00 \, \text{m}$
• New length ($L'$): $10.05 \, \text{m}$
• Goal: Calculate the Young's Modulus ($E$).

2. Explain the concept

Young's Modulus ($E$) is defined as the ratio of Stress to Strain.

• Stress ($\sigma$): Force per unit area ($\frac{F}{A}$).
• Strain ($\epsilon$): The ratio of the change in length ($\Delta L$) to the original length ($L$). • $\text{Strain} = \frac{\Delta L}{L}$
• Formula: $E = \frac{\text{Stress}}{\text{Strain}} = \frac{\sigma}{\Delta L / L}$

3. Show the solution

Step 1: Calculate the change in length ($\Delta L$)

Step 2: Calculate the Strain ($\epsilon$)

Step 3: Calculate Young's Modulus ($E$)

To simplify this, treat the numbers and powers of 10 separately:

To express this in standard form:

4. Identify the answer

Comparing our result to the options provided, the correct value is $2.0 \times 10^9 \, \text{Nm}^{-2}$. This matches option D.

5. Tip

When dealing with Young's Modulus questions, always ensure your units are consistent (meters for length). If you see a very small strain, don't panic—the resulting Young's Modulus is usually a very large number, which is typical for materials like steel or copper.