Question

Find the greatest length of steel wire that can hang vertically without breaking.Breaking stress of steel =8.0xx10^(8) N//m^(2). Density of steel =8.0xx10^(3) kg//m^(3). Take g =10 m//s^(2).

Answer 1

Therefore the length of the steel wire is 10 Km.

Explanation:

Breaking stress: The stress applied on a material is the ratio of weight of the material to the cross section area.

$stress=\frac{weight}{\textrm{ Cross section area}}$

Given , $\sigma_m$ = Breaking stress= $8\times 10^8 \ N/m^2$

gravity = g = 10 m/s²

$\rho$= density $=8\times 10^3 \ kg/m^3$

Weight

=mass × gravity

= $\rho$×v×g

=$\rho$ × A × l × g  [ A= cross section area, l = the length]

Therefore

$\sigma_m= \frac{\rho \times A \times l \times g}{A}$

$\Rightarrow \sigma_m=\rho \times l \times g$

$\Rightarrow l=\frac{\sigma_m}{\rho \times g}$

Putting the value of $\sigma_m$, g and $\rho$

$\therefore l=\frac{8.0\times 10^8}{8.0\times 10^3 \times 10}$ kg

     $=10^4$ m.

    =10 km.

Therefore the length of the steel wire is 10 Km.