Extension via Young's modulus formula

Steps:

• Convert units: L = 300 cm = 3 m, A = 0.5 mm² = 5 × 10^{-7} m².
• Apply formula ΔL = (F L) / (A Y), where F = 10 N, Y = 2 × 10^{11} Pa.
• Compute numerator: F L = 10 × 3 = 30 N·m.
• Compute ΔL: denominator A Y = 5 × 10^{-7} × 2 × 10^{11} = 1 × 10^5; ΔL = 30 / 10^5 = 3 × 10^{-4} m.

Why C is correct:

• Matches extension from Young's modulus Y = (F/A) / (ΔL/L), rearranged to ΔL = (F L) / (A Y).

Why the others are wrong:

• A: Too small; error in area conversion (e.g., used 0.5 m² instead of 5 × 10^{-7} m²).
• B: Too small by factor of 10; likely forgot to convert length from cm to m.
• D: Too large by factor of 100; probably used area in mm² without converting to m².

Final answer: C