If the cross-sectional radius of a wire under tension is doubled, how is its Young’s modulus affected_______________?
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Answer: E. remain unaffected
Explanation
Young's modulus is an intrinsic material property independent of the wire's cross-sectional dimensions or radius. Doubling the cross-sectional radius changes the cross-sectional area and stiffness, but the material's elastic modulus remains constant. Modulus of elasticity depends solely on atomic bonding forces within the specific metal alloy composition. Young's modulus is defined as the ratio of tensile stress to engineering tensile strain within the elastic region. Intrinsic material properties do not change regardless of specimen size, shape, length, or cross-sectional area. Hooke's law applies uniformly across metallic wires of varying thicknesses subjected to tensile loads.
Structural engineers rely on constant material property values when designing cables, wires, and support rods. Changing wire thickness alters overall stiffness and elongation under load, but the material stiffness constant stays fixed. Metallurgical testing confirms that elastic moduli remain uniform across different manufactured wire gauges. Doubling the radius does not double Young's modulus, as elastic constants are entirely independent of geometry. Halving the modulus would violate fundamental metallurgical and solid mechanics material science principles. Multiplying or dividing the modulus by four incorrectly confuses intrinsic material constants with cross-sectional area.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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