The dimensions of four wires of the same material are given...

The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum? (a) Length $100 \mathrm{~cm}$, Diameter $1 \mathrm{~mm}$ (b) Length $200 \mathrm{~cm}$, Diameter $2 \mathrm{~mm}$ (c) Length $300 \mathrm{~cm}$, Diameter $3 \mathrm{~mm}$ (d) Length $50 \mathrm{~cm}$, Diameter $0.5 \mathrm{~mm}$

The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum?
(a) Length $100 \mathrm{~cm}$, Diameter $1 \mathrm{~mm}$
(b) Length $200 \mathrm{~cm}$, Diameter $2 \mathrm{~mm}$
(c) Length $300 \mathrm{~cm}$, Diameter $3 \mathrm{~mm}$
(d) Length $50 \mathrm{~cm}$, Diameter $0.5 \mathrm{~mm}$

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Key Concepts

Dependence on Length and Cross-Sectional Area

The extension of a wire under a tensile force is directly proportional to its original length and inversely proportional to its cross-sectional area. This means a longer wire or a wire with a smaller cross-sectional area (which, for a circular cross-section, depends on the square of the diameter) will experience a greater increase in length when the same force is applied.

Geometric Influence on Deformation

The diameter of a wire influences its cross-sectional area since the area of a circular cross-section is proportional to the square of the diameter. Thus, small changes in diameter can significantly affect the wire's ability to resist deformation under tensile stress.

Young's Modulus

Young's modulus is a fundamental material property that quantifies the stiffness of a material by relating stress (force per unit area) to strain (relative deformation). It governs how much a material stretches or compresses under a given load within the elastic limit.

Stress and Strain

Stress represents the force applied per unit area on a material, while strain is the measure of the deformation experienced by the material relative to its original dimensions. The linear relationship between stress and strain, as described by Hooke’s law, is key in understanding elastic deformation.

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