Question

An iron wire of length 4 m and diameter 2 mm is loaded with a weight of 8 kg. if the young's modulus 'Y' for iron is $2*10^11 Nm^-2 then the increase in length of the wire is

• A. 0.2 mm
• B. 0.5 mm
• C. 2 mm
• D. 1 mm

Answer 1

The correct option is B 0.5 mm

Given,

$g=9.8m/s^2$

$m=8kg$

$l=4m$

$D=2mm$

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

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

Young's modulus of the iron wire,

$Y=\frac{F/A}{\Delta l/l}$

$\Delta l=l\frac{mg}{Y\pi r^2}$

$\Delta =4\times \frac{8\times 9.8}{2\times {10}^{11}\times 3.14\times (1\times {10}^{-3}{)}^2}$

$\Delta l=0.5mm$

The correct option is B.