A steel wire and a copper wire of equal length and equal cross sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of a. The stresses developed in the two wire and b. the strains developed. Y of steel `=2xx10^11Nm^-2`. Y of copper `=1.3xx10^11 Nm^-2`.

Explanation

To solve the problem, we need to find the ratio of stresses and strains developed in a steel wire and a copper wire that are joined end to end and subjected to tension.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two wires: one steel and one copper.
- Both wires are of equal length (L) and equal cross-sectional area (A).
- They are connected end to end and subjected to the same tension (T).

2. **Finding the Stress in Each Wire**:
- Stress is defined as the force (tension) per unit area.
- For both wires, the stress (σ) can be calculated using the formula:
\[ \text{Stress} = \frac{T}{A} \]
- Since both wires are under the same tension and have the same cross-sectional area, the stresses in the steel wire (σ_steel) and the copper wire (σ_copper) are equal:
\[ \sigma_{steel} = \sigma_{copper} = \frac{T}{A} \]
- Therefore, the ratio of stresses is:
\[ \frac{\sigma_{steel}}{\sigma_{copper}} = 1 \]

3. **Finding the Strain in Each Wire**:
- Strain (ε) is defined as the change in length per unit original length.
- Using Young's modulus (Y), we know:
\[ Y = \frac{\text{Stress}}{\text{Strain}} \implies \text{Strain} = \frac{\text{Stress}}{Y} \]
- For the steel wire:
\[ \epsilon_{steel} = \frac{\sigma_{steel}}{Y_{steel}} = \frac{\frac{T}{A}}{2 \times 10^{11}} \]
- For the copper wire:
\[ \epsilon_{copper} = \frac{\sigma_{copper}}{Y_{copper}} = \frac{\frac{T}{A}}{1.3 \times 10^{11}} \]
- Now, we can find the ratio of strains:
\[ \frac{\epsilon_{steel}}{\epsilon_{copper}} = \frac{\frac{T/A}{2 \times 10^{11}}}{\frac{T/A}{1.3 \times 10^{11}}} = \frac{1.3 \times 10^{11}}{2 \times 10^{11}} = \frac{1.3}{2} = \frac{13}{20} \]

### Final Results:
- **a. Ratio of Stresses**:
\[ \frac{\sigma_{steel}}{\sigma_{copper}} = 1 \]
- **b. Ratio of Strains**:
\[ \frac{\epsilon_{steel}}{\epsilon_{copper}} = \frac{13}{20} \]