The Young's modulus of a wire of length L and radius r is Y. If the length and radius is reduced to L/2 and r/2 respectively, then its Young' modulus will be

Options

A. `Y//2`
B. Y
C. 2Y
D. 4Y

Explanation

To determine the Young's modulus of a wire when its length and radius are reduced, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Young's Modulus**:
Young's modulus (Y) is defined as the ratio of stress to strain in a material. It is a property of the material itself and does not change with the dimensions of the wire.

2. **Initial Conditions**:
Let the initial length of the wire be \( L \) and the radius be \( r \). The Young's modulus of this wire is given as \( Y \).

3. **Change in Dimensions**:
The length of the wire is reduced to \( \frac{L}{2} \) and the radius is reduced to \( \frac{r}{2} \).

4. **Effect on Young's Modulus**:
Since Young's modulus is a material property, it remains constant regardless of the changes in length and radius. Therefore, even after reducing the dimensions of the wire, the Young's modulus remains the same.

5. **Conclusion**:
Thus, the Young's modulus of the wire after reducing its length and radius will still be \( Y \).

### Final Answer:
The Young's modulus of the wire after reducing its length to \( \frac{L}{2} \) and radius to \( \frac{r}{2} \) will be \( Y \).

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