(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

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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

The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass $2.96 \ kg$ and density $7.4 \ g \ cm^{-3}$ is (Young's modulus of steel $= 2 \times 10^{11} \ Nm^{-2}$)

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When a small mass $m$ is suspended at the lower end of an elastic wire having its upper end fixed to a ceiling,there is a loss in gravitational potential energy,let it be $x$,due to the extension of the wire. Mark the correct option.

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$A$ uniform metal rod of $2\, mm^2$ cross-section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of the rod is $12 \times 10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of the rod will be ....... $J/m^3$.

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$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

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Work done in stretching a wire through $1 \ mm$ is $2 \ J$. What amount of work will be done for elongating another wire of same material,with half the length and double the radius of cross-section,by $1 \ mm$ (in $J$)?

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The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass $2.96 \ kg$ and density $7.4 \ g \ cm^{-3}$ is (Young's modulus of steel $= 2 \times 10^{11} \ Nm^{-2}$)

When a small mass $m$ is suspended at the lower end of an elastic wire having its upper end fixed to a ceiling,there is a loss in gravitational potential energy,let it be $x$,due to the extension of the wire. Mark the correct option.

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

Work done in stretching a wire through $1 \ mm$ is $2 \ J$. What amount of work will be done for elongating another wire of same material,with half the length and double the radius of cross-section,by $1 \ mm$ (in $J$)?

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