Question

A wire of length $2\text{m}$ is suspended from the top of a roof at one end and a load of $W$ is attached at the other end. Cross-sectional area of the wire is $5\times {10}^{-7}{\text{m}}^2$ and elongation $\left(\Delta l\right)$ is shown in the graph. Find the Young's modulus of elasticity of the wire material.

• A. $1\times {10}^{11}{\text{N/m}}^2$
• B. $1.6\times {10}^{12}{\text{N/m}}^2$
• C. $2\times {10}^{11}{\text{N/m}}^2$
• D. $4\times {10}^{11}{\text{N/m}}^2$

Answer 1

The correct option is D $4\times {10}^{11}{\text{N/m}}^2$

Young's modulus of elasticity is given by
$Y=\frac{\text{stress}}{\text{strain}}$

Note: Young's modulus is only valid till proportionality limit.
$Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}=\frac{Fl}{A\Delta l}$
From the graph, we can see $\Delta l=2\times {10}^{-4}\text{m}$ when $F=50\text{N}$
$\Rightarrow Y=\frac{20\times 2}{5\times {10}^{-7}\times 2\times {10}^{-4}}=4\times {10}^{11}{\text{N/m}}^2$