Question

The graph showing the extension of is wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. of the cross-sectional area of the wire is $1{mm}^2$, then the Young's modulus of the material of the wire .( In graph, X-axis 1 unit = 10mm) .

• A. $2\times {10}^{11}N{m}^{-1}$
• B. $2\times {10}^{10}N{m}^{-2}$
• C. $\frac{1}{2}\times {10}^{11}N{m}^{-2}$
• D. None of these

Answer 1

The correct option is B $2\times {10}^{10}N{m}^{-2}$

Let $Y$ denote the Young's Modulus.
Then
$Y\frac{△L}{L_0}=\frac{F}{A}$
$L=1m$ , $A={10}^{-6}m$
Hence
$Y(\frac{(5-1)\times {10}^{-3}}{m}1m=\frac{100-20N}{{10}^{-6}{m}^2}$
$Y(4\times {10}^{-3})=80\times {10}^{6}N{m}^{-2}$
$Y=20\times {10}^{9}N{m}^{-2}$
$=2\times {10}^{10}N{m}^{-2}$