(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

$A$ stress of $1.5 \, kg.wt/mm^2$ is applied to a wire of Young's modulus $5 \times 10^{11} \, N/m^2$. The percentage increase in its length is

Medium

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The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be

Easy

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$A$ force is applied to a steel wire '$A$',rigidly clamped at one end. As a result,the elongation in the wire is $0.2\,mm$. If the same force is applied to another steel wire '$B$' of double the length and a diameter $2.4$ times that of the wire '$A$',the elongation in the wire '$B$' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections).

MediumJEE MAIN 2023

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$A$ steel rod of length $1\,m$ and cross-sectional area $10^{-4}\,m^2$ is heated from $0^{\circ}C$ to $200^{\circ}C$ without being allowed to extend or bend. The compressive force produced in the rod is $........\times 10^4\,N$. (Given: Young's modulus of steel $Y = 2 \times 10^{11}\,N/m^2$,coefficient of linear expansion $\alpha = 10^{-5}\,K^{-1}$)

EasyJEE MAIN 2023

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$A$ weight of $200 \, kg$ is suspended by a vertical wire of length $600.5 \, cm$. The area of cross-section of the wire is $1 \, mm^2$. When the load is removed,the wire contracts by $0.5 \, cm$. The Young's modulus of the material of the wire will be:

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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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$A$ stress of $1.5 \, kg.wt/mm^2$ is applied to a wire of Young's modulus $5 \times 10^{11} \, N/m^2$. The percentage increase in its length is

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be

$A$ weight of $200 \, kg$ is suspended by a vertical wire of length $600.5 \, cm$. The area of cross-section of the wire is $1 \, mm^2$. When the load is removed,the wire contracts by $0.5 \, cm$. The Young's modulus of the material of the wire will be:

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