Question

Find the greatest length of steel wire that can hang vertically without breaking. Breaking stress of steel is ${\sigma }_m$ and the density of wire is $\rho$.

• A. $\frac{{\sigma }_m}{\rho g}$
• B. $\frac{2{\sigma }_m}{\rho g}$
• C. $\frac{3{\sigma }_m}{\rho g}$
• D. $\frac{4{\sigma }_m}{\rho g}$

Answer 1

The correct option is A $\frac{{\sigma }_m}{\rho g}$

Let $l$ be the length of the wire that can hang vertically without breaking.

The stretching force on the wire is equal to its own weight.

If $A$ is the area of cross-section and $\rho$ is the density, then

$\text{Maximum stress,}{\sigma }_m=\frac{\text{Weight}}{\text{Cross-sectional Area}}$

${\sigma }_m=\frac{\left(Al\rho \right)g}{A}$

$\therefore l=\frac{{\sigma }_m}{\rho g}$

Hence, option $\left(\text{A}\right)$ is correct.

$\text{Key Concept:}$ Breaking stress is the maximum force that can be applied on a cross-sectional area of a material in such a way that the material is unable to withstand any additional amount of stress before breaking. Breaking stress may also be known as ultimate tensile stress or breaking strength.