Length of a rod is 20, cm and area of cross-section 2,c{m^2} . Young's modulus of material of wi

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8.Mechanical Properties of Solids

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

$8.57 \times {10^{ - 6}}$

$22.5 \times {10^{ - 4}}$

$9.8 \times {10^{ - 5}}$

$45.0 \times {10^{ - 5}}$

Solution

(a) Energy = $\frac{1}{2}Fl = \frac{1}{2} \times F \times \left( {\frac{{FL}}{{AY}}} \right) = \frac{1}{2} \times \frac{{{F^2}L}}{{AY}}$

$ = \frac{1}{2} \times \frac{{{{(50)}^2} \times 20 \times {{10}^{ – 2}}}}{{2 \times {{10}^{ – 4}} \times 1.4 \times {{10}^{11}}}}$$ = 8.57 \times {10^{ – 6}}J$

Standard 11

Physics

A metal wire having Poisson's ratio $1 / 4$ and Young's modulus $8 \times 10^{10} \,N / m ^2$ is stretched by a force, which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in wire is [in $\left.J / m ^3\right]$

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What is called elastic potential energy ? Write its different formulas.

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A uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If modulus of rigidity of the wire is $\eta$, then the elastic potential energy stored in wire, is ………

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Calculate the work done, if a wire is loaded by $'Mg'$ weight and the increase in length is $'l'$

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

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(JEE MAIN-2023)

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

Solution

Similar Questions

A metal wire having Poisson's ratio $1 / 4$ and Young's modulus $8 \times 10^{10} \,N / m ^2$ is stretched by a force, which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in wire is [in $\left.J / m ^3\right]$

What is called elastic potential energy ? Write its different formulas.

A uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If modulus of rigidity of the wire is $\eta$, then the elastic potential energy stored in wire, is ………

Calculate the work done, if a wire is loaded by $'Mg'$ weight and the increase in length is $'l'$

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

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