Question

The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied. (A) Length $100 \mathrm{~cm}$, Diameter $1 \mathrm{~mm}$ (B) Length $200 \mathrm{~cm}$, Diameter $2 \mathrm{~mm}$ (C) Length $300 \mathrm{~cm}$, Diameter $3 \mathrm{~mm}$ (D) Length $50 \mathrm{~cm}$, Diameter $0.5 \mathrm{~mm}$

Name: Problem 840, Chapter 7: JEE Physics
Uploaded: 2021-11-09T05:03:45-08:00
Duration: 1 min 47 s
Channel: Sachin Rao
Description: The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied. (A) Length 100 cm, Diameter 1 mm (B) Length 200 cm, Diameter 2 mm (C) Length 300 cm, Diameter 3 mm (D) Length 50 cm, Diameter 0.5 mm

   The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied.
(A) Length $100 \mathrm{~cm}$, Diameter $1 \mathrm{~mm}$
(B) Length $200 \mathrm{~cm}$, Diameter $2 \mathrm{~mm}$
(C) Length $300 \mathrm{~cm}$, Diameter $3 \mathrm{~mm}$
(D) Length $50 \mathrm{~cm}$, Diameter $0.5 \mathrm{~mm}$

JEE Physics

StemEZ 1st Edition

Chapter 7, Problem 840

Instant Answer

Solved by Expert Sachin Rao

11/09/2021

Step 1

Also, the same strain is applied to all wires. We know that Young's modulus is equal to stress divided by strain, which can be written as $\frac{\Delta L}{L} = \frac{F}{A} \cdot \frac{1}{Y}$, where $\Delta L$ is the change in length, $L$ is the original length, Show more…

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The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied. (A) Length $100 \mathrm{~cm}$, Diameter $1 \mathrm{~mm}$ (B) Length $200 \mathrm{~cm}$, Diameter $2 \mathrm{~mm}$ (C) Length $300 \mathrm{~cm}$, Diameter $3 \mathrm{~mm}$ (D) Length $50 \mathrm{~cm}$, Diameter $0.5 \mathrm{~mm}$

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Key Concepts

Strain

Strain is the measure of deformation representing the fractional change in length of a material when a force is applied. It is defined as the ratio of the change in length (?L) to the original length (L), making it a dimensionless quantity that allows comparison of deformation irrespective of the size of the sample.

Relationship Between Strain and Extension

When the same strain is applied to different materials, the absolute change in length (extension) is directly proportional to the original length of the material. This means that, for a given strain, a longer sample undergoes a larger increase in length, since ?L = strain × original length.

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