Question

If velocity (V), force(F) and time(t) are taken to be fundamental quantities and K is the dimensionless constant of proportionality, find the dimensional formula for mass.

• A. [KVFT]
• B. $\left[K{V}^{-2}FT\right]$
• C. $\left[K{V}^{-1}FT\right]$
• D. $\left[K{V}^{-1}F{T}^2\right]$

Answer 1

The correct option is C

$\left[K{V}^{-1}FT\right]$

Let dimensional formula of mass be $M=K\left[V{]}^a\right[F{]}^b[t{]}^c$
Now, dimension of velocity, $\left[V\right]=\left[L{T}^{-1}\right]$
Dimension of force, $\left[F\right]=\left[ML{T}^{-2}\right]$
Dimension of time $=\left[T\right]$
Solving we get, $a=-1,b=1$ and $c=1$
So, $\left[M\right]=\left[K{V}^{-1}FT\right]$