Question

If $\mathrm{S}$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is $[\mathbf{2 0 0 5}]$ (A) $2 S^{2} Y$ (B) $\frac{S^{2}}{2 Y}$ (C) $\frac{2 Y}{S^{2}}$ (D) $\frac{S}{2 Y}$

Name: Problem 103, Chapter 8: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-07T04:56:10-08:00
Duration: 1 min 5 s
Channel: Mahipal Kumawat
Description: If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is [2 0 0 5] (A) 2 S^2 Y (B) (S^2)/(2 Y) (C) (2 Y)/(S^2) (D) (S)/(2 Y)

   If $\mathrm{S}$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is $[\mathbf{2 0 0 5}]$
(A) $2 S^{2} Y$
(B) $\frac{S^{2}}{2 Y}$
(C) $\frac{2 Y}{S^{2}}$
(D) $\frac{S}{2 Y}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 8, Problem 103

Instant Answer

Solved by Expert Mahipal Kumawat

10/07/2021

Step 1

Step 1: The energy stored per unit volume in a wire is given by the formula $\frac{1}{2} \times \text{stress} \times \text{strain}$. Show more…

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If $\mathrm{S}$ is stress and $Y$ is Young's modulus of material of a wire, the energy stored in the wire per unit volume is $[\mathbf{2 0 0 5}]$ (A) $2 S^{2} Y$ (B) $\frac{S^{2}}{2 Y}$ (C) $\frac{2 Y}{S^{2}}$ (D) $\frac{S}{2 Y}$

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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 to strain in the elastic region of the material's stress-strain curve. This modulus helps predict how much a material will stretch or compress under a given load.

Elastic Energy Density

Elastic energy density refers to the energy stored per unit volume in a material during elastic deformation. It is determined by the work done to deform the material, often represented as the area under the stress-strain curve in the elastic regime. In linear elastic materials, this typically relates to the square of the stress divided by twice the Young's modulus.

Stress

Stress is a measure of the internal force per unit area within materials when they are subjected to external forces. It is fundamental in understanding how materials respond to loads, and it plays a critical role in the analysis of material deformation and failure.

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