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

Let l be the wire that can hang vertically without breaking. The stretching force on it is equal to its own weight.
If A is the area of cross-section and `rho` is the density, then
Maximum stress `(sigma_(m))=("weight")/(A)" "(because " stress"=("force")/("area"))`
Weight `=mg=Vrhog`(`because` Mass =Volume `xx` density)
`=Alrhog`
(`because`=Volume =area of cross-section `xx` heigth)
or `sigma_(m)=((Alrho)g)/(A)" "(because rho=(m)/(V))`
`therefore` Length of the steel wire, `l=(sigma_(m))/(rhog)`
`l=(8xx10^(8))/((8xx10^(3))(10))=10^(4)m`