Question

A metal wire of length $1m$ and cross-section area $2m{m}^2$ and Young's modulus of elasticity $Y=4\times {10}^{11}N/m^2$ is stretched by $2mm$. Then

• A. the restoring force developed in the wire is $1600N$
• B. the energy density in the wire is $4\times {10}^{5}J/m^3$
• C. the restoring force developed in the wire is $400N$
• D. the total elastic energy stored in the wire is $1.6J$

Answer 1

The correct option is A the restoring force developed in the wire is $1600N$

$L=1m$

$\alpha =2{mm}^2=\left(\frac{2}{{\left(1000\right)}^2}\right)=2\times {10}^{-6}m$

$Y=4\times {10}^{11}N/m^2$

$\Delta l=2mm=\frac{2}{10.00}=0.002m$

$F=\frac{Y\alpha l}{L}$

$=\frac{4\times {10}^{11}\times 2\times {10}^{-6}\times 2\times {10}^{-3}}{1m}$

$=16\times {10}^{11-6-3}$

$=16\times {10}^{11-9}$

$=16\times {10}^2$

$=1600N$

Where $\alpha =$ cross sectional area $=2\times {10}^{-6}m$

$l=2mm=2\times {10}^{-3}m$

$L=1m$