The Young’s modulus of a wire of length L and radius r is Y N/m². If the length and radius are reduced to L/2 and r/2, then its Young’s modulus will be

The correct answer is Y.

Explanation:
Young's modulus ($Y$) is defined as the ratio of tensile (or compressive) stress to longitudinal strain:

$Y=\frac{\text{Stress}}{\text{Strain}}$

Young’s modulus is an intrinsic, characteristic property of the material of the wire. It depends strictly on the nature of the material and its temperature, and it is entirely independent of the geometry or physical dimensions (such as the length $L$ or cross-sectional area/radius $r$) of the wire.

Therefore, when the length is reduced to $\frac{L}{2}$ and the radius is reduced to $\frac{r}{2}$, the material of the wire does not change. Consequently, its Young’s modulus remains unchanged at $Y$.