Question

The Young's modulus of a wire of length $L$ and $r a d$ is $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ then the Young's modulus will be (a) $\frac{Y}{2}$ (b) $Y$ (c) $2 Y$ (d) $4 Y$

Name: Problem 58, Chapter 9: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-25T13:45:35-08:00
Duration: 59 s
Channel: Kamlesh Goyal
Description: The Young's modulus of a wire of length L and r a d is r is Y. If the length is reduced to (L)/(2) and radius is (r)/(2) then the Young's modulus will be (a) (Y)/(2) (b) Y (c) 2 Y (d) 4 Y

   The Young's modulus of a wire of length $L$ and $r a d$ is $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ then the Young's modulus will be
(a) $\frac{Y}{2}$
(b) $Y$
(c) $2 Y$
(d) $4 Y$

Objective NCERT at your FINGERTIPS: Physics

NCERT 11th Edition

Chapter 9, Problem 58

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Solved by Expert Kamlesh Goyal

09/25/2021

Step 1

Step 1: The Young's modulus of a material is given by the formula $Y = \frac{F/A}{\Delta L/L}$, where $F$ is the force applied, $A$ is the cross-sectional area, $\Delta L$ is the change in length, and $L$ is the original length. Show more…

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The Young's modulus of a wire of length $L$ and $r a d$ is $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ then the Young's modulus will be (a) $\frac{Y}{2}$ (b) $Y$ (c) $2 Y$ (d) $4 Y$

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Key Concepts

Young's Modulus

Young's modulus is a fundamental material property that quantifies the stiffness of a material by defining the ratio of stress (force per unit area) to strain (relative change in length). It is an intrinsic parameter, meaning it is inherent to the material itself and does not depend on the sample's size or shape.

Intrinsic Material Properties

Intrinsic material properties are characteristics inherent to a material that do not change with the geometry or amount of material. They are determined by the material’s internal structure and bonding. Since Young's modulus is intrinsic, altering the dimensions such as length or radius of a sample will not affect its value.

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