Question

A steel wire is 1m long and 1$m{m}^2$ in the area of cross-section. If it takes $200N$ to stretch the wire by $1mm$, the force that will be required to stretch the wire of the same material and cross-sectional area from a length of $10m$ to $1002cm$

• A. $100N$
• B. $200N$
• C. $400N$
• D. $2000N$

Answer 1

Answer: (C)

$400N$

$Y=\frac{Fl}{A△l}$
$Y=\frac{200\times 1}{{10}^{-6}\times {10}^{-3}}$
$Y=2\times {10}^{11}$
$△l=1002-1000=2cm,l=10m$
$F=\frac{YA△l}{l}$
$=\frac{2\times {10}^{11}\times {10}^{-6}\times 2\times {10}^{-2}}{10}$
$=400N$