Question

The dimensional formula for Young's modulus is:

• A. $\left[M{L}^{-1}{T}^{-2}\right]$
• B. $\left[M^{0}L{T}^{-2}\right]$
• C. $\left[ML{T}^{-2}\right]$
• D. $\left[M{L}^2{T}^{-2}\right]$

Answer 1

Answer: (A)

When strain is small, the ratio of the longitudinal tress to the corresponding longitudinal strain is called Young's modulus of the material of the body.
$Y=\frac{\text{ stress }}{\text{ strain }}=\frac{\frac{F}{A}}{\frac{l}{L}}$
Where $F$ is force, $A$ is area, $l$ and $L$ are change in length and original length.
Dimensions of $Y=\frac{\left[M{L}^{-1}{T}^{-2}\right]}{\left[M^{\circ }{L}^{\circ }{T}^{\circ }\right]}$
$=\left[M{L}^{-1}{T}^{-2}\right]$
Alternative: The SI unit of $Y$ is $N{m}^{-2}$ or Pascal.
Therefore,
Dimensions of $Y=\frac{\text{ newton }}{{\text{ metre }}^2}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}$
$=\left[M{L}^{-1}{T}^{-2}\right]$