(C) The formula for Young's modulus $(Y)$ is given by $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{l/L} = \frac{FL}{Al}$.Rearranging this for

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Increase in length is inversely proportional to $A$.

(C) The formula for Young's modulus $(Y)$ is given by $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{l/L} = \frac{FL}{Al}$.Rearranging this formula to solve for the increase in length $(l)$,we get:$l = \frac{FL}{YA}$.From this expression,it is clear that the increase in length $(l)$ is directly proportional to the force $(F)$ and the original length $(L)$,and inversely proportional to the Young's modulus $(Y)$ and the area of cross-section $(A)$.Therefore,$l \propto \frac{1}{A}$.Thus,the correct statement is that the increase in length is inversely proportional to $A$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Easy

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

A
Increase in length is inversely proportional to its length $L$.
B
Increase in length is proportional to the area of cross-section $A$.
C
Increase in length is inversely proportional to $A$.
D
Increase in length is proportional to Young's modulus.

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Class 11

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Chapter

Mechanical Properties of Solids

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Young’s Modulus

$A$ load of mass $M \ kg$ is suspended from a steel wire of length $2 \ m$ and radius $1.0 \ mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0 \ mm$. Now,the load is fully immersed in a liquid of relative density $2$. The relative density of the material of the load is $8$. The new value of increase in length of the steel wire is ........ $mm$.

DifficultJEE MAIN 2019

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The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

MediumIIT 2003

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If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be:

Difficult

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$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

MediumMHT CET 2019

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The area of cross-section of a wire of length $1.1 \, m$ is $1 \, mm^2$. It is loaded with $1 \, kg$. If Young's modulus of copper is $1.1 \times 10^{11} \, N/m^2$,then the increase in length will be ......... $mm$ (Take $g = 10 \, m/s^2$)

Medium

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The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

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The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

If the ratio of length,radii,and Young's modulus of steel and aluminium wire are $a, b, c$ respectively,then the corresponding ratio of increase in their length would be:

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

The area of cross-section of a wire of length $1.1 \, m$ is $1 \, mm^2$. It is loaded with $1 \, kg$. If Young's modulus of copper is $1.1 \times 10^{11} \, N/m^2$,then the increase in length will be ......... $mm$ (Take $g = 10 \, m/s^2$)

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