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The elongation of a material is directly proportional to its length and inversely proportional to its cross-sectional area, assuming which factors remain unchanged?

1. The force applied and Young's modulus are constant.
2. The elongation is proportional to length and inversely proportional to the square of the diameter.
3. The elongation is proportional to length and inversely proportional to the cross-sectional area.
4. The extension depends on both the length and the cross-sectional area in an inverse relationship.

Correct answer: The force applied and Young's modulus are constant.

Solution

The extension (ΔL) of a material is directly proportional to its original length (L) and inversely proportional to its cross-sectional area (A), provided the force (F) and Young's modulus (Y) are constant. This follows from the formula ΔL = (F × L) / (A × Y).

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