The following wires A, B, C, D, are made of the same material with diff. length and diameter. Wh

step 1 My friends, Young's modulars of the material is F into capital L divided by A into L. Here, Y is

The following wires A, B, C, D, are made of the same...

The following wires $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$, are made of the same material with diff. length and diameter. Which of these will have the largest extension, when the same tension is applied? (A) length $=200 \mathrm{~cm}$, diameter $=2 \mathrm{~mm}$ (B) length $=50 \mathrm{~cm}$, diameter $=0.5 \mathrm{~mm}$ (C) length $=300 \mathrm{~cm}$, diameter $=3 \mathrm{~mm}$ (D) length $=100 \mathrm{~cm}$, diameter $=1 \mathrm{~mm}$

The following wires $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$, are made of the same material with diff. length and diameter. Which of these will have the largest extension, when the same tension is applied?
(A) length $=200 \mathrm{~cm}$, diameter $=2 \mathrm{~mm}$
(B) length $=50 \mathrm{~cm}$, diameter $=0.5 \mathrm{~mm}$
(C) length $=300 \mathrm{~cm}$, diameter $=3 \mathrm{~mm}$
(D) length $=100 \mathrm{~cm}$, diameter $=1 \mathrm{~mm}$

Key Concepts

Cross-sectional Area and Diameter Relationship

For wires with circular cross-sections, the cross-sectional area is proportional to the square of the diameter. As the diameter increases, the area increases quadratically, which decreases the extension under a constant load. Understanding this relationship is key in comparing the elastic responses of different wires.

Geometrical Factors in Elastic Deformation

The extension of a wire is influenced by its original length and cross-sectional area, following the relation ?L = (F × L) / (A × E). A longer wire or a wire with a smaller cross-sectional area will experience a greater extension when the same force is applied, illustrating the pivotal role of geometry in elastic deformation.

Young’s Modulus

Young’s modulus is a material constant that measures the stiffness of a material. It defines the relationship between tensile stress and tensile strain in a material under elastic deformation. For wires made of the same material, this constant remains unchanged, allowing comparisons of extension based solely on other factors like length and cross-sectional area.

Hooke’s Law

Hooke’s law states that, within the elastic limit of a material, the extension of a wire is directly proportional to the applied force, provided the material’s elastic properties remain constant. This principle is fundamental when evaluating how different wires extend under the same tension.

Tensile Stress and Strain

Tensile stress is defined as the force per unit cross-sectional area, and tensile strain is the ratio of the change in length to the original length. The proportionality between stress and strain, mediated by Young’s modulus, explains how a material deforms under a given load.

Transcript

Please give Ace some feedback