The resistance of the new wire is D. 400 Ω
How to find the resistance ?
In this case, the resistivity and the cross-sectional area remain the same because the wire is melted and recasted from the same material. However, the length is doubled (L' = 2L).
Therefore:
R' = ρ * L' / A²
= ρ * (2L) / A ²
= 2 * (ρ * L / A ²)
= 2 * R
Since the wire is doubled in length but presumably not doubled in width or thickness (assuming it was originally cylindrical), the cross-sectional area will be reduced by half. This will further increase the resistance.
Accounting for both the increase in length and the decrease in area, the new resistance becomes:
R' = ρ * (2L) / (A/2) ²
= 4 * (ρ * L / A ²)
= 4 * R
= 4 x 100
= 400 Ω