Question

If $x$ is longitudinal strain produced in a wire of Young's modulus $Y$, then energy stored in the material of the wire per unit volume is (a) $Y x^{2}$ (b) $2 Y \underline{x^{2}}$ (c) $\frac{1}{2} \gamma^{2} x$ (d) $\frac{1}{2} Y x^{2}$

Name: Problem 12, Chapter 11: Master Resource Book in JEE Main Physics
Uploaded: 2022-02-20T01:38:34-08:00
Duration: 1 min 9 s
Channel: Yuva S
Description: If x is longitudinal strain produced in a wire of Young's modulus Y, then energy stored in the material of the wire per unit volume is (a) Y x^2 (b) 2 Y x^2 (c) (1)/(2) γ^2 x (d) (1)/(2) Y x^2

   If $x$ is longitudinal strain produced in a wire of Young's modulus $Y$, then energy stored in the material of the wire per unit volume is
(a) $Y x^{2}$
(b) $2 Y \underline{x^{2}}$
(c) $\frac{1}{2} \gamma^{2} x$
(d) $\frac{1}{2} Y x^{2}$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 11, Problem 12

Instant Answer

Solved by Expert Yuva S

02/20/2022

Step 1

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

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If $x$ is longitudinal strain produced in a wire of Young's modulus $Y$, then energy stored in the material of the wire per unit volume is (a) $Y x^{2}$ (b) $2 Y \underline{x^{2}}$ (c) $\frac{1}{2} \gamma^{2} x$ (d) $\frac{1}{2} Y x^{2}$

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Key Concepts

Strain Energy Density

Strain energy density is the energy stored per unit volume in a material due to deformation. For a material obeying linear elasticity, the work done to produce a strain is given by the area under the stress-strain curve. Because the stress and strain are linearly related by Young's modulus, this area—representing the energy per unit volume—is calculated as one half times Young’s modulus multiplied by the square of the strain.

Young's Modulus

Young’s modulus is a fundamental material property that quantifies the stiffness of a material. It is defined as the ratio of stress to strain in the region where the material exhibits linear elastic behavior. This property plays a crucial role in determining how much energy is stored in a material when it is deformed.

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