A and B are two wires. The radius of A is twice that of B. They are stretched by the some load. The the stress on B is

Options

A. Equal to that on A
B. Four times that on A
C. Two times that on A
D. Half that on A

Answer

To solve the problem, we need to compare the stress experienced by two wires, A and B, given that the radius of wire A is twice that of wire B and both wires are subjected to the same load.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Let the radius of wire B be \( r \).
- Therefore, the radius of wire A is \( R_A = 2r \).
- Both wires are subjected to the same force \( F \).

2. **Understand the Formula for Stress:**
- Stress (\( \sigma \)) is defined as the force applied per unit area.
- The formula for stress is:
\[ \sigma = \frac{F}{A} \]
- For a circular cross-section, the area \( A \) is given by:
\[ A = \pi r^2 \]

3. **Calculate the Cross-Sectional Areas:**
- For wire A:
\[ A_A = \pi (R_A)^2 = \pi (2r)^2 = 4\pi r^2 \]
- For wire B:
\[ A_B = \pi (r)^2 = \pi r^2 \]

4. **Calculate the Stress in Each Wire:**
- For wire A:
\[ \sigma_A = \frac{F}{A_A} = \frac{F}{4\pi r^2} \]
- For wire B:
\[ \sigma_B = \frac{F}{A_B} = \frac{F}{\pi r^2} \]

5. **Express the Stress Ratio:**
- To compare the stresses, we can take the ratio of stress in wire B to stress in wire A:
\[ \frac{\sigma_B}{\sigma_A} = \frac{\frac{F}{\pi r^2}}{\frac{F}{4\pi r^2}} = \frac{4\pi r^2}{\pi r^2} = 4 \]
- Therefore, we can conclude that:
\[ \sigma_B = 4 \sigma_A \]

6. **Conclusion:**
- The stress on wire B is 4 times the stress on wire A.

### Final Answer:
The stress on wire B is 4 times the stress on wire A.

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