Question

The dimensional formula of $\frac{slug}{bam}$ is:

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

Answer 1

The correct option is B $\left[M^1{L}^{-2}{T}^0\right]$

Slug is a unit of mass ,equivalent to $14.59kg$ and Barn is a unit of surface area, equivalent to ${10}^{-28}{m}^2$.

So,
Dimension of slug $=$ Dimension of mass $=\left[M\right]$Dimension of barn $=$ Dimension of area $=\left[L^2\right]$
Then
Dimensional formula of $\frac{Slug}{Barn}=\frac{\left[M\right]}{\left[L^2\right]}=\left[M^1{L}^{-2}{T}^0\right]$