Question

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

• A. $2\times {10}^{11}N/m^2$
• B. $2\times {10}^{-11}N/m^2$
• C. $3\times {10}^{12}N/m^2$
• D. $2\times {10}^{13}N/m^2$

Answer 1

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

Given:

Length, $L=1m$

Area of crossection, $A={10}^{-6}{m}^2$

From above graph at load of 20 N the extention is $\Delta L=1\times {10}^{-4}{m}^2$

We know that, $Y=\frac{Fl}{A\Delta l}$

putting values in above equation

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