Question

A substance breaks down by a stress of $10^{6} N / m ^{2}$. If the density of the material of the wire is $3 \times 10^{3} kg / m ^{3}$, then the length of the wire of the substance which will break under its own weight when suspended vertically, is:

• A. 66.6m
• B. 60.0m
• C. 33,3m
• D. 30.0m

Answer 1

Answer: (C)

If an external force $F$ is applied to the cross-sectional area $A$ of the body, then
Stress $=\frac{F}{A}=\frac{m g}{A}$
where mass in = volume $x$ density $=A l \rho$
Stress $=\frac{A l \rho g}{A}=\rho l g$
$=l=\frac{\text { breakingstress }}{\rho g}$
Given breaking stress $=10^{6}\, Nm ^{-2}$
$\rho=3 \times 10^{3} \,kgm ^{-3}, $
$g=10 \,ms ^{-2}$
$=l=\frac{10^{6}}{\left(3 \times 10^{3}\right) \times 10}$
$I =33.3 \,m$