Question

A wire has a breaking stress of $6 \times 10^{5} \,N / m ^{2}$ and a density of $3 \times 10^{4} \,kg / m ^{3}$. The length of the wire of the same material which will break under its own weight, (if $g=10 \,m / s ^{2}$ ) is

• A. 2000 m
• B. 2500 m
• C. 20 m
• D. 2 m

Answer 1

Answer: (D)

Breaking stress is given by
$=6 \times 10^{5} \,N / m ^{2}=\frac{m g}{A}$
(But $m=A L \rho$ )
$6 \times 10^{5}=\frac{A L \rho g}{A}=L \rho g $
Thus, $L=\frac{6 \times 10^{5}}{\rho g}=\frac{6 \times 10^{5}}{3 \times 10^{4} \times 10}=2 \,m$