Question

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

• A. $2\times {10}^{11}N/m$
• B. $2\times {10}^{-11}N/m$
• C. $2\times {10}^{-12}N/m$
• D. $2\times {10}^{-13}N/m$

Answer 1

The correct option is A $2\times {10}^{11}N/m$

$Y=\frac{FL}{Al}$

$Y=\frac{W\times 1}{{10}^{-6}\times \Delta l}$

$Y=\frac{1}{{10}^{-6}\times \frac{\Delta l}{W}}$

From the graph we can see the slope of $\frac{\Delta l}{W}$ $=\frac{{10}^{-4}}{20}$

$Y=\frac{1}{{10}^{-6}\times \frac{{10}^{-4}}{20}}=20\times {10}^{10}=2\times {10}^{11}N/m^2$