Question

A wire of length $1\text{m}$ and area of cross-section $4\times {10}^{-8}{\text{m}}^2$ increase in length by $0.2\text{cm}$ when a force of $16\text{N}$ is applied. The value of $Y$ for the material of the wire will be

• A. $2\times {10}^6{\text{N/m}}^2$
• B. $2\times {10}^5{\text{N/m}}^2$
• C. $2\times {10}^{12}{\text{N/m}}^2$
• D. $2\times {10}^{11}{\text{N/m}}^2$

Answer 1

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

Using Hook's law, we have

$Y=\frac{FL}{Al}=\frac{16\times 1}{(4\times {10}^{-8})(0.2\times {10}^{-2})}=2\times {10}^{11}{\text{N/m}}^2$

Hence, $\left(D\right)$ is the correct answer.

Why this question? Young's Modulus of Elasticity: It is defined as the ratio of the normal stress to the longitudinal strain. That is $\text{Young's modulus (Y)}=\frac{\text{Longitudinal stress}}{\text{Longitudinal strain}}$