Assertion If length of a wire is halved, its Young's modulus of elasticity will become two times.
Reason The ratio of longitudinal stress and longitudinal strain is called Young's modulus of elasticity.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question regarding the assertion and reason about Young's modulus of elasticity, we will analyze both statements step by step.

### Step-by-step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (E) is defined as the ratio of longitudinal stress (σ) to longitudinal strain (ε). Mathematically, it is expressed as:
\[ E = \frac{\sigma}{\epsilon} \]
where:
- Longitudinal stress (σ) = \(\frac{F}{A}\) (Force per unit area)
- Longitudinal strain (ε) = \(\frac{\Delta L}{L_0}\) (Change in length/original length)

2. **Analyzing the Assertion**:
The assertion states that if the length of a wire is halved, its Young's modulus of elasticity will become two times.
- Young's modulus is a material property and does not depend on the dimensions of the material, such as length or cross-sectional area.
- Therefore, halving the length of the wire will not change its Young's modulus. It remains constant regardless of the wire's length.

3. **Conclusion on Assertion**:
Since Young's modulus is independent of the length of the wire, the assertion is **false**.

4. **Analyzing the Reason**:
The reason states that the ratio of longitudinal stress to longitudinal strain is called Young's modulus of elasticity.
- This statement is correct. Young's modulus is indeed defined as the ratio of stress to strain.

5. **Conclusion on Reason**:
The reason is **true**.

6. **Final Evaluation**:
Since the assertion is false and the reason is true, we conclude that the correct relationship is:
- Assertion: False
- Reason: True

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