Stretching a thin wire

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Problem: Stretching a thin wire
A wire has length 2 m, area 1.0 mm² and Young modulus 2.0 × 10¹¹ Pa. A 100 N tensile force acts.
Question: Find its extension.
Givens:
- L = 2 m
- A = 10⁻⁶ m²
- Y = 2×10¹¹ Pa
- F = 100 N
Assumptions: Uniform Hookean wire under axial tension; small strain, constant area and Young modulus; neglect self-weight.
Choices (LaTeX):
A. 2\times10^{-3}\ \mathrm m
B. 1.0\times10^{-3}\ \mathrm m
C. 1\ \mathrm m
D. 0.5\times10^{-3}\ \mathrm m

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.