Following tour wires ot length L and raduk are made of the...

following tour wires ot length $L$ and raduk are made of the same material. Which of these will have the largest extension, when the same tension is applied? (a) $L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}$ (b) $L=200 \mathrm{~cm}, r=0.4 \mathrm{~mm}$ (c) $L=300 \mathrm{~cm}, r=0.6 \mathrm{~mm}$ (d) $L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}$

following tour wires ot length $L$ and raduk are made of the same material. Which of these will have the largest extension, when the same tension is applied?
(a) $L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}$
(b) $L=200 \mathrm{~cm}, r=0.4 \mathrm{~mm}$
(c) $L=300 \mathrm{~cm}, r=0.6 \mathrm{~mm}$
(d) $L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}$

Key Concepts

Hooke's Law

Hooke’s Law describes the behavior of elastic materials by stating that the extension of a material is directly proportional to the force applied to it, as long as the material’s elastic limit is not exceeded. This principle underlies many calculations in mechanics and material science involving deformation under load.

Young’s Modulus

Young’s Modulus is a material property that quantifies the stiffness of an elastic material, relating stress (force per unit area) to strain (relative change in length). It is used in the formula for elastic extension and is constant for a given material, allowing comparisons of deformation for different geometries.

Stress and Strain

Stress is the force applied per unit area of a material, while strain is the relative deformation or extension resulting from that force. The relationship between stress and strain in elastic materials is linear, as described by Young’s Modulus, which is key for calculating how materials deform under tension.

Geometric Factors in Elastic Deformation

The extension of a wire under tension not only depends on the material properties but also on its geometry. Specifically, the extension is directly proportional to the length of the wire and inversely proportional to its cross-sectional area. The cross-sectional area, which for a circular wire is proportional to the square of the radius, plays a critical role in determining how much a wire will stretch under a given load.

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