Question

The breaking stress of aluminium is $7.5\times 10^{7}N{m}^{-2}$ . Find the greatest length of aluminium wire that can hang vertically without breaking . Density of aluminium is $2.7\times 10^3{Kgm}^{-3}$.

Answer 1

Given,

$\sigma =7.5\times {10}^{7}N/m^2$

$\rho =2.7\times {10}^{3}kg/m^3$

Lets consider the maximum length of aluminium wire that can be hang vertically without breaking is $l$

Volume of wire,

$V=Al$

Mass of wire,

$M=\rho V=\rho Al$

When hung force acting on the wire,

$F=mg=\rho Alg$. . . . . . .(1)

$\frac{F}{A}=\rho lg$

$\sigma =\rho lg$

$l=\frac{\sigma }{\rho g}=\frac{7.5\times {10}^7}{9.8\times 2.7\times {10}^3}$

$l=2.83\times {10}^{3}m$