Question

The dimensional formula of modulus of elasticity is

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

Answer 1

The correct option is A $\left[{ML}^{-1}{T}^{-2}\right]$

Modules of elasticity $=\frac{stress}{strain}$
Stress $=\frac{\left[F\right]}{\left[A\right]}=\frac{\left[{MLT}^{-2}\right]}{\left[L^2\right]}=\left[{ML}^{-1}{T}^{-2}\right]$
Strain is a dimensionless quantity.

So, modules of elasticity = $\left[{ML}^{-1}{T}^{-2}\right]$