Question

An iron wire of length $4m$ and diameter $2mm$ is loaded with a weight of $8kg$. If the young's modulus '$Y$' for iron is $2$ x $10$${}^{11}$ N/m${}^2$, then the increase in the length of the wire is

• A. $0.2mm$
• B. $0.5mm$
• C. $2mm$
• D. $1mm$

Answer 1

The correct option is B $0.5mm$

$Y=\frac{Fl}{A\Delta l}$

$\Delta l=\frac{Fl}{AY}$

$=\frac{80\times l}{r{\left(\frac{2}{2}\right)}^2\times {10}^{-6}\times 2\times {10}^{11}}$

$=5.0\times {10}^{-4}m$

$=0.5mm$