(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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Mechanical Properties of Solids

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Young’s Modulus

Two masses $m_1$ and $m_2$ are connected by a light string passing over a pulley as shown in the figure. If the cross-sectional area of the string is $S$,its length is $L$,and its Young's modulus is $Y$,what is the elongation in the string?

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$A$ structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ $A$ $100\,kN$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11}\,N/m^2.$ The percentage strain is about ....... $\%$

MediumAIEEE 2012

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As shown in the figure,a light uniform rod $PQ$ of length $150 \ cm$ is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2:3$ and $3:2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is

MediumAP EAMCET 2025

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$A$ wire of length $2 \ m$ and cross-sectional area $10^{-2} \ cm^2$ is fixed at one end. $A$ force of $200 \ N$ is applied at the other end. The coefficient of linear expansion of the wire is $1.1 \times 10^{-5} \ ^oC^{-1}$ and the Young's modulus is $1.2 \times 10^{11} \ N/m^2$. If the temperature is increased by $10^oC$,what will be the thermal stress developed in the wire?

Difficult

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$A$ force $F$ is applied to a wire of length $L$ and radius $r$,resulting in an extension $l$. What will be the extension in a wire of length $2L$ and radius $2r$ when a force $2F$ is applied?

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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Two masses $m_1$ and $m_2$ are connected by a light string passing over a pulley as shown in the figure. If the cross-sectional area of the string is $S$,its length is $L$,and its Young's modulus is $Y$,what is the elongation in the string?

$A$ structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ $A$ $100\,kN$ force stretches it along its length. Young's modulus of structural steel is $2 \times 10^{11}\,N/m^2.$ The percentage strain is about ....... $\%$

$A$ force $F$ is applied to a wire of length $L$ and radius $r$,resulting in an extension $l$. What will be the extension in a wire of length $2L$ and radius $2r$ when a force $2F$ is applied?

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