Assertion: Every wire is like a spring, whose spring constant ,`K prop 1/l`, where l is length of wire.
Reason : It follows from the relation
`K = (YA)/(l)`

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.

Answer

To solve the problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that every wire behaves like a spring, and its spring constant \( K \) is inversely proportional to its length \( l \). This means that as the length of the wire increases, the spring constant decreases.

### Step 2: Understanding the Reason
The reason provided is based on the formula for the spring constant \( K \) given by:
\[ K = \frac{YA}{l} \]
where:
- \( Y \) is the Young's modulus of the material,
- \( A \) is the cross-sectional area of the wire,
- \( l \) is the length of the wire.

### Step 3: Analyzing the Formula
From the formula \( K = \frac{YA}{l} \), we can see that:
- \( K \) is directly proportional to the Young's modulus \( Y \) and the cross-sectional area \( A \),
- \( K \) is inversely proportional to the length \( l \).

This implies that if the length \( l \) increases, the spring constant \( K \) decreases, confirming the assertion.

### Step 4: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that:
- The assertion is true.
- The reason is true and provides the correct explanation for the assertion.

### Final Answer
Both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

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