(A) Given: Length $L = 20 \, cm = 0.2 \, m$,Area $A = 2 \, cm^2 = 2 \times 10^{-4} \, m^2$,Young's modulus $Y = 1.4 \times 10^{11} \, N/m^2$,Force $F

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(A) Given: Length $L = 20 \, cm = 0.2 \, m$,Area $A = 2 \, cm^2 = 2 \times 10^{-4} \, m^2$,Young's modulus $Y = 1.4 \times 10^{11} \, N/m^2$,Force $F = 5 \, kg-wt = 5 \times 9.8 \, N = 49 \, N$ (taking $g = 9.8 \, m/s^2$).The elastic potential energy $U$ stored in a rod is given by the formula:$U = \frac{1}{2} \times \frac{F^2 L}{AY}$Substituting the values:$U = \frac{1}{2} \times \frac{(49)^2 \times 0.2}{2 \times 10^{-4} \times 1.4 \times 10^{11}}$$U = \frac{1}{2} \times \frac{2401 \times 0.2}{2.8 \times 10^7}$$U = \frac{480.2}{5.6 \times 10^7} \approx 8.57 \times 10^{-6} \, J$.

Class 11 Physics Mechanical Properties of Solids Work Done in Stretching a Wire

Medium

The length of a rod is $20 \, cm$ and the area of cross-section is $2 \, cm^2$. The Young's modulus of the material of the rod is $1.4 \times 10^{11} \, N/m^2$. If the rod is compressed by a force of $5 \, kg-wt$ along its length,then the increase in the elastic potential energy of the rod in joules will be:

A
$8.57 \times 10^{-6}$
B
$22.5 \times 10^{-4}$
C
$9.8 \times 10^{-5}$
D
$45.0 \times 10^{-5}$

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Mechanical Properties of Solids

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Work Done in Stretching a Wire

What is the work done in stretching a uniform metal wire of length $2 \ m$ to $2.004 \ m$ with an area of cross-section $10^{-6} \ m^2$ (in $J$)? [Young's modulus of the wire = $2 \times 10^{11} \ N/m^2$]

EasyTS EAMCET 2022

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Work done by the restoring force in a string within the elastic limit is $-10 \, J$. The maximum amount of heat produced in the string is .......... $J$.

Easy

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The elastic potential energy stored in a steel wire of length $20 \, m$ stretched by $2 \, cm$ is $80 \, J$. The cross-sectional area of the wire is $......... \, mm^2$ (Given,$Y = 2.0 \times 10^{11} \, N/m^2$).

MediumJEE MAIN 2023

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$A$ wire is suspended by one end. At the other end,a weight equivalent to $20\, N$ force is applied. If the increase in length is $1.0\, mm$,the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when the load moves downwards by $1\, mm$ will be:

Medium

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$A$ copper wire of length $3 \text{ m}$ is stretched by $3 \text{ mm}$ by applying an external force. The volume of the wire is $600 \times 10^{-6} \text{ m}^3$. The elastic potential energy stored in the wire in the stretched condition is . . . . . . $\text{J}$. (Given Young's modulus of copper $Y = 1.1 \times 10^{11} \text{ N/m}^2$)

DifficultJEE MAIN 2026

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What is the work done in stretching a uniform metal wire of length $2 \ m$ to $2.004 \ m$ with an area of cross-section $10^{-6} \ m^2$ (in $J$)? [Young's modulus of the wire = $2 \times 10^{11} \ N/m^2$]

Work done by the restoring force in a string within the elastic limit is $-10 \, J$. The maximum amount of heat produced in the string is .......... $J$.

The elastic potential energy stored in a steel wire of length $20 \, m$ stretched by $2 \, cm$ is $80 \, J$. The cross-sectional area of the wire is $......... \, mm^2$ (Given,$Y = 2.0 \times 10^{11} \, N/m^2$).

$A$ wire is suspended by one end. At the other end,a weight equivalent to $20\, N$ force is applied. If the increase in length is $1.0\, mm$,the ratio of the increase in energy of the wire to the decrease in gravitational potential energy when the load moves downwards by $1\, mm$ will be:

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