A steel wire is 1m long and 1mm² in area of cross-section. If it takes 200 N to stretch this wire by 1mm how much force will be required to stretch the wire of the same area and of same material having length of 10m to 1002 cm $\_\_\_\_$N
 

Given,

$\mathrm{F}=200\mathrm{N}, \mathrm{L}=1\mathrm{m}, \mathrm{A}=1{\mathrm{mm}}^2={10}^{-6}{\mathrm{m}}^2, \mathrm{\Delta L}=1\mathrm{mm}={10}^{-3}\mathrm{m}$

We can determine the Young's modulus' value by entering all these values as substitutes in the formula:

$\mathrm{Y}=\frac{\mathrm{F}l}{\mathrm{A}∆l}=\frac{200\times 1}{{10}^{-6}\times {10}^{-3}}=2\times {10}^{11}$

$∆l=1002-1000=2\mathrm{cm}$

$l=10\mathrm{m}$

$\mathrm{F}=\frac{\mathrm{YA}∆l}{l}=\frac{2\times {10}^{11}\times {10}^{-6}\times 2\times {10}^{-2}}{10}=400\mathrm{N}$

Hence the correct answer 400N.