Question

Find the greatest length of steel wire that can hang vertically without breaking stress of steel =8×10^8N/m^2 density 8×10^3kg/m^3 g=10m/s^2

Answer 1

Check the attachment

Answer 2

Answer:

The greatest length of the steel wire to which it can hang vertically is $10^{4}\ m$

Explanation:

The breaking stress of the steel wire is $\sigma_{b}=8\times 10^{8}\ N/m^2$

The density of the steel wire is $\rho_{s}=8\times 10^{3}\ kg/m^3$

we know that the stress is equal to the force per unit area

The cross section area of the steel wire is A

The length of the steel wire is l

The force on the free hanging steel wire is due to its weight

The weight of the steel wire is

$F=Al\rho g$

We know that,

$\sigma_{b}=\dfrac{F}{A}\\\sigma_{b}=\dfrac{Al\rho g}{A}\\\sigma_{b}=l\rho g\\l=\dfrac{\sigma_{b}}{\rho g}\\l=\dfrac{8\times 10^{8}}{8\times 10^{3}\times 10}\\l=10^{4}\ m$