Assertion: From the relation Y `= (Fl)/(ADeltal)`, we can say that, if length of a wire is doubled, its young's modulus of elasticity will also becomes two times.
Reason : Modulus of elasticity is a material property.

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 solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that from the relation \( Y = \frac{Fl}{A \Delta l} \), if the length of a wire is doubled, its Young's modulus of elasticity will also become two times.

**Analysis**:
- Young's modulus \( Y \) is defined as the ratio of stress to strain.
- Stress is defined as \( \frac{F}{A} \) (force per unit area), and strain is defined as \( \frac{\Delta l}{l} \) (change in length per original length).
- From the formula \( Y = \frac{Fl}{A \Delta l} \), if we double the length \( l \), we must also consider how the change in length \( \Delta l \) behaves.

### Step 2: Understand the Reason
The reason states that modulus of elasticity is a material property.

**Analysis**:
- Young's modulus is indeed a material property, meaning it is intrinsic to the material itself and does not depend on the dimensions of the material (like length or area).
- Therefore, regardless of the length of the wire, the Young's modulus for a specific material remains constant.

### Step 3: Conclusion
Since the assertion incorrectly states that doubling the length of the wire will double its Young's modulus, while the reason correctly identifies that Young's modulus is a material property, we can conclude:

- **Assertion**: False
- **Reason**: True

### Final Answer
The correct option is that the assertion is false and the reason is true.

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