Assertion : identical springs of steel and copper are equally stretched. More work will be done on the steel spring.
Reason : Steel is more elastic than copper.

Options

A. (a) If both Assertion and Reason are true and the Reason is correctn explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To analyze the assertion and reason provided in the question, we need to understand the concepts of elasticity, Young's modulus, and how they relate to the work done on springs made of different materials.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that if identical springs made of steel and copper are equally stretched, more work will be done on the steel spring.

2. **Understanding Work Done on Springs**:
The work done (W) on a spring when it is stretched can be expressed using Hooke's Law:
\[ W = \frac{1}{2} k x^2 \]
where \( k \) is the spring constant and \( x \) is the extension.

3. **Comparing Spring Constants**:
The spring constant \( k \) is related to the material's Young's modulus \( Y \) and the dimensions of the spring. For a spring, the spring constant is given by:
\[ k = \frac{Y A}{L} \]
where \( A \) is the cross-sectional area and \( L \) is the original length of the spring.

4. **Material Properties**:
Steel generally has a higher Young's modulus than copper, meaning it is more resistant to deformation. Therefore, for the same dimensions, the spring constant \( k \) for steel will be greater than that for copper.

5. **Calculating Work Done**:
Since the assertion claims that both springs are equally stretched, we can denote the extension \( x \) as the same for both springs. Thus, the work done on each spring can be expressed as:
- For steel: \( W_{steel} = \frac{1}{2} k_{steel} x^2 \)
- For copper: \( W_{copper} = \frac{1}{2} k_{copper} x^2 \)

6. **Conclusion on Work Done**:
Since \( k_{steel} > k_{copper} \), it follows that:
\[ W_{steel} > W_{copper} \]
Therefore, more work is indeed done on the steel spring than on the copper spring, confirming the assertion.

7. **Understanding the Reason**:
The reason states that steel is more elastic than copper. This is true because elasticity is often quantified by Young's modulus, which is higher for steel compared to copper.

8. **Final Evaluation**:
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and the reason are true, and the reason correctly explains the assertion.

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