Write the unit and dimensional formula of modulus of elasticity.

(N/A) The modulus of elasticity $(Y)$ is defined as the ratio of stress to strain.
$Y = \frac{\text{Stress}}{\text{Strain}}$
Since strain is a dimensionless quantity (ratio of change in dimension to original dimension),the unit and dimensions of the modulus of elasticity are the same as those of stress.
Stress is defined as force per unit area: $\text{Stress} = \frac{F}{A}$.
The $SI$ unit of force is Newton $(N)$ and the $SI$ unit of area is square meter $(m^2)$.
Therefore,the $SI$ unit of modulus of elasticity is $N/m^2$ or Pascal $(Pa)$.
The dimensional formula for force is $[M^1 L^1 T^{-2}]$ and for area is $[L^2]$.
Thus,the dimensional formula for modulus of elasticity is $\frac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]$.