If rho is the density of the material of a wi | vedclass

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(D) Let the length of the wire be $\ell$ and its cross-sectional area be $A$.The weight of the wire acts as the force $F$ causing stress, where $F = \

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$\frac{\sigma}{\rho g}$

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(D) Let the length of the wire be $\ell$ and its cross-sectional area be $A$.The weight of the wire acts as the force $F$ causing stress, where $F = 	ext{mass} 	imes g = (	ext{Volume} 	imes 	ext{density}) 	imes g = (A \ell) ho g$.The stress $\sigma$ is defined as the force per unit area: $\sigma = \frac{F}{A}$.Substituting the expression for $F$: $\sigma = \frac{(A \ell) ho g}{A}$.Simplifying the equation: $\sigma = \ell ho g$.Therefore, the maximum length $\ell$ that can hang without breaking is: $\ell = \frac{\sigma}{ho g}$.

If $\rho$ is the density of the material of a wire and $\sigma$ is the breaking stress, what is the greatest length of the wire that can hang freely without breaking?

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