Question

A force of $6 \times 10^{6} Nm ^{-2}$ required for breaking a material. The density $\rho$ of the material is $3 \times 10^{3} kg m ^{-3}$. If the wire is to break under its own weight, the length of the wire made of that material should be (take $g=10 \,ms ^{-2}$ )

• A. 20 m
• B. 200 m
• C. 100 m
• D. 2000 m

Answer 1

Answer: (B)

When a wire is pulled it stretches (undergoes strain) upto a certain limit the amount it stretches is proportional to the load divided by the cross-sectional area of the wire.
Stress $=\frac{\text { Force }}{\text { Area }}=\frac{m g}{A}=\frac{V \rho g}{A}=\frac{L A \rho g}{A}$
$\therefore $ Stress $=L \rho g$
Given, stress $=6 \times 10^{6} Nm ^{-2} $
$\rho =3 \times 10^{3} kg m ^{-3}$
$g =10 \,ms ^{-2} $
$L =\frac{\text { stress }}{\rho g} $
$=\frac{6 \times 10^{6}}{3 \times 10^{3} \times 10} $
$=2 \times 10^{2}=200 \,m$