Compute the greatest length of steel wire that can hang vertically without breaking under its own weight. (Breaking stress of steel wire $7.2 \times 10^{8} N / m^{2}$ ,density of steel $= 7800 k g / m^{3}$ )

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Solution

At point $B$ , stress will be maximum and will be equal to $\frac{w e i g h t}{A r e a}$
$\Rightarrow (s t r e s s)_{B} = \frac{m \times g}{A} = (ρ) \frac{A . l g}{A}$
$= ρ l g$
At Breaking point,
$(s t r e s s)_{B}$ =Breaking stress
$\Rightarrow ρ l g = B . S \Rightarrow l = \frac{7.2 \times 10^{8}}{(7800) (10)}$
$\Rightarrow l = 9230.77 m$

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