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 $Y=\frac{\text { newton }}{\text { metre }^{2}}=\frac{\left[M L T^{-2}\right]}{\left[L^{2}\right]}$
$=\left[ ML ^{-1} T ^{-2}\right]$