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  • A wire breaks when subjected to a stress S. If is the density of the material of the wire and

A wire breaks when subjected to a stress S. If \mathrm{\rho} is the density of the material of the wire and g, the acceleration due to gravity, then the length of the wire so that it breaks by its own weight is

Option: 1

\mathrm{\rho g S}


Option: 2

\mathrm{\frac{\rho g}{S}}


Option: 3

\mathrm{\frac{g S}{\rho}}


Option: 4

\mathrm{\frac{S}{\rho g}}


Answers (1)

best_answer

Let L be the required length of wire. If A is its area of cross-section and \rho is the density of its material, the weight of the wire is

\mathrm{ \begin{gathered} W=m g=A L \rho g \\\\ \therefore \quad \text { Stress }=\frac{\text { weight }}{\text { area }}=\frac{A L \rho g}{A}=L \rho g \\\\ \text { or } \quad S=L \rho g \Rightarrow L=S / \rho g \end{gathered} }

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Nehul

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