Question

A steel wire, $3.2m$ long, has a diameter of $1.2mm$. The wire stretches by $1.6mm$ when it bears a load. Young's modulus for steel is $2.0\times 10^{11}Pa$. The mass of the load is closest to:

• A. 24 kg
• B. 28 kg
• C. 12 kg
• D. 20 kg

Answer 1

Answer: (C)

We know that
$\frac{F}{A}=Y\frac{\Delta l}{l}$
$\Rightarrow \frac{mg}{A}=Y\frac{\Delta l}{l}$
i.e. $m=\frac{A}{g}Y\frac{\Delta l}{l}$
$=\frac{\pi {\left(0.6\times 10^{-3}\right)}^2\times 2\times 10^{11}\times 1.6\times 10^{-3}}{10\times 3.2}$
$=\frac{0.36\pi }{10}\times 10^2=3.6\pi \approx 11.3$
$\therefore$ closest mass $=12kg$