Question

If length ${}^{\prime }{L}^{\prime }$, force ${}^{\prime }{F}^{\prime }$ and time ${}^{\prime }{T}^{\prime }$ are takes as fundamental quantities. What would the dimensional equation of mass and density?

Answer 1

Let us apply the equation,

$F=ma$

Apply the fundamental units.

Thus,

$F=mass\times L{T}^{-2}mass=\frac{F}{L{T}^{-2}}=F{L}^{-1}{T}^2$

Similarly,

$density=\frac{mass}{volume}=\frac{F{L}^{-1}{T}^2}{L^3}=F{L}^{-4}{T}^2$