Question

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Young's modulii of the materials, then (a) $Y_{B}=2 Y_{A}$ (b) $Y_{A}=Y_{B}$ (c) $Y_{B}=3 Y_{A}$ (d) $Y_{A}=3 Y_{B}$

Name: Problem 30, Chapter 9: Objective Physics for NEET
Uploaded: 2021-09-18T17:07:56-08:00
Duration: 1 min 15 s
Channel: Dheeraj Sharma
Description: The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If YA and YB are the Young's modulii of the materials, then (a) YB=2 YA (b) YA=YB (c) YB=3 YA (d) YA=3 YB

   The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Young's modulii of the materials, then
(a) $Y_{B}=2 Y_{A}$
(b) $Y_{A}=Y_{B}$
(c) $Y_{B}=3 Y_{A}$
(d) $Y_{A}=3 Y_{B}$

Objective Physics for NEET

Abhay Kumar 1st Edition

Chapter 9, Problem 30

Instant Answer

Solved by Expert Dheeraj Sharma

09/18/2021

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We need to find the relation between the Young's moduli of these two materials. We know that Young's modulus is given by the ratio of stress to strain. Show more…

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The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Young's modulii of the materials, then (a) $Y_{B}=2 Y_{A}$ (b) $Y_{A}=Y_{B}$ (c) $Y_{B}=3 Y_{A}$ (d) $Y_{A}=3 Y_{B}$

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Key Concepts

Young's Modulus

Young's modulus is a material property that quantifies the stiffness of a material. It is defined as the ratio of stress (force per unit area) to strain (relative deformation) within the elastic limit, and is determined from the slope of the linear portion of a stress–strain graph.

Stress–Strain Graph

A stress–strain graph plots the applied stress against the resulting strain on a material. The graph’s initial linear segment reflects elastic behavior, where the material deforms reversibly, and its slope gives a direct measure of the Young's modulus.

Hooke's Law

Hooke's law states that, for small deformations within the elastic limit of a material, the stress applied is directly proportional to the strain produced. This linear relationship underpins the analysis of materials using stress–strain graphs and the determination of Young's modulus.

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