Question

The adjacent graph shows the extension (l) of a wire of length 1 m suspended from the top of a roof at one end and with load 'W' connected to the other end. If the cross-sectional area of the wire is ${10}^{-6}$$m^{-2}$, calculate the Young modulus of the material of the wire:

• A. $2\times {10}^{-11}$
• B. $2\times {10}^{10}$
• C. $2\times {10}^{11}$
• D. $2\times {10}^{-10}$

Answer 1

The correct option is C $2\times {10}^{11}$

From the graph if we choose a point for which $W=40N$ and correspondingly $△L=2\times {10}^{-4}m$

Also given,

$A={10}^{-6}{m}^2$

$l=1m$

$\therefore$ Youngs modulus,$Y=\frac{\frac{F}{A}}{\frac{△l}{l}}$

putting values we get,

$Y=\frac{F\times l}{A\times △l}$

$=\frac{40\times 1}{{10}^{-6}\times 2\times {10}^{-4}}$

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