Question

Give the MKS units for Young's modulus

• A. $N{m}^{-3}$
• B. $N{m}^{-2}$
• C. $N{m}^{-4}$
• D. $N/2m^{-2}$

Answer 1

Answer: (B)

$N{m}^{-2}$

$Y=\frac{\text{stress}}{\text{Strain}}=\frac{f/A}{\frac{\Delta l}{l}}=\frac{F}{A}\times \left(\frac{l}{\Delta l}\right)$

$\begin{array}{c}Y=\left(\frac{f}{A}\right)\left(\frac{\Delta l}{l}\right)\\ Y=\left(\frac{F}{A}\right)\end{array}$

$\begin{array}{c}\text{Unit of force = Newton}\\ \text{unit of Area}={\text{(meler)}}^2\end{array}$

$\therefore Y_{\text{unit}}=\frac{M}{m^2}=N{m}^{-2}$

Hence option B is correct