Young's modulus of material of a wire of length $$L$$ and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modulus will be:

Young's modulus is a material property that depends only on the nature of the material, not on the dimensions of the wire.

By definition, Young's modulus is: $$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$$

While stress and strain depend on the dimensions (length $$L$$ and cross-sectional area $$A$$), the ratio $$Y$$ is an intrinsic property of the material itself. Therefore, if the length is doubled and the cross-sectional area is halved, the Young's modulus remains unchanged at $$Y$$.

Option Y