Question

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

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

Answer 1

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

The applied load $=F=mg=2\times 9.8=19.6N$

diameter $=1mm=1\times {10}^{-3}m$

=> radius$=0.5\times {10}^{-7}m$

Area , $A=3.14r^2=3.14\times 0.25\times {10}^{-6}$

$=0.785\times {10}^{-6}$

We know that$,$

$stress=Force/area$

$=19.6/0.785\times {10}^{-6}$

$24.96\times {10}^{-6}$

change in length$,\Delta L=1mm={10}^{-3}m$

Length$,L=3m$

$hencestrain=\Delta L/L$

$={10}^{-3}/3$

we know that young's modulus is given by the ratio of stress and strain$,$

Hence$,$

$E=24.96\times {10}^{-6}/{10}^{-3}/3$

$=74.8\times {10}^9$

$=7.48\times {10}^{10}N{m}^{-2}$

Hence,

option $\left(C\right)$ is correct answer.