Question

A mass of $1$kg is hung from a steel wire of radius $0.5$mm and length $4$m. Calculate the extension produced. What should be the area of cross-section of the wire so that elastic limit is not exceeded? Change in radius is negligible. (Given: $g=9.8m/s^2;$ Elastic limit of steel is $2.4\times {10}^{8}N/m^2;$ Y for steel $\left(Y_{steel}\right)=20\times {10}^{10}N/m^2;\pi =3.142$).

Answer 1

A mass of m=1kg and weight F=10 N is hung from a steel wire of radius r=0.5mm and length L= 4m.
$Y=20\times {10}^{10}N/m^2$
Area A=$\pi r^2=7.8\times {10}^{-7}{m}^2$
Elongation , $dl=\frac{FL}{AY}=\frac{10\times 4}{20\times {10}^{10}\times 7.8\times {10}^{-7}}=0.25mm$
A elastic limit, the wire can withstand maximum stress.
$\frac{F}{A}=2.4\times {10}^{8}N/m^2$
A is the area of cross section
A=$4.17\times {10}^{-8}{m}^2$