Question

A load of $2kg$ produces an extension of $1mm$ in wire of $3m$ in length and $1mm$ in diameter. The Young's modulus of wire will be

• A. $3.25\times {10}^{10}N{m}^{-2}$
• B. $7.48\times {10}^{12}N{m}^{-2}$
• C. $7.48\times {10}^{10}N{m}^{-2}$
• D. $7.48\times {10}^{-10}N{m}^{-2}$

Answer 1

The correct option is C $7.48\times {10}^{10}N{m}^{-2}$

Given,

$m=2kg$

$l=3m$

$g=9.8m/s^2$

$\Delta l=1mm={10}^{-3}m$

$d=1mm$

$r=0.5\times {10}^{-3}m$

Stress, $s=\frac{F}{A}=\frac{mg}{\pi r^2}$

$s=\frac{2\times 9.8}{3.14\times (0.5\times {10}^{-3}{)}^2}=24.96\times {10}^{6}N/m^2$

strain, $st=\frac{\Delta l}{l}=\frac{1\times {10}^{-3}}{3}$

Young's modulus, $Y=\frac{stress}{strain}$

$Y=\frac{24.96\times {10}^6}{{10}^{-3}/3}=7.48\times {10}^{10}N/m^2$

The correct option is C.