Young's modulus definition Steps:

• Recall stress σ = F / A, where F is force and A is area.
• Recall strain ε = ΔL / L, where ΔL is change in length and L is original length.
• Young's modulus E is defined as the ratio of stress to strain: E = σ / ε.
• Substitute definitions: E = (F / A) / (ΔL / L) = (F L) / (A ΔL).

Why A is correct:

• Directly matches the definition E = σ / ε, the standard formula for Young's modulus.

Why the others are wrong:

• B: F / ΔL represents stiffness but ignores area and original length, not Young's modulus.
• C: ΔL / L is strain ε alone, not the modulus.
• D: F / (A σ) simplifies to 1, which is dimensionless and incorrect.

Final answer: A