Question

If velocity $\left(V\right)$, force $\left(F\right)$ and time $\left(T\right)$ are taken to be fundamental quantity and $K$ is the dimensionless constant of proportionality, find dimensional formula for mass.

• A. $\left[KVFT\right]$
• 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 $\left[K{V}^{-1}FT\right]$

As per the question let $M$ be the quantity
$M=K{V}^x{F}^y{T}^z\dots \left(i\right)$
Dimension of velocity $V=\left[L^1{T}^{-1}\right]$
Dimension of force $F=\left[M^1{L}^1{T}^{-2}\right]$
Dimension of time $T=\left[T^1\right]$
Now from equation $\left(i\right)$
$\left[M\right]=\left[L{T}^{-1}{]}^x\right[ML{T}^{-2}{]}^y[T{]}^z$
Equating the exponents $y=1$
$x+y=0$ and $-x-2y+z=0$
On solving $x=-1,y=1$ and $z=1,$
So, $M=\left[K{V}^{-1}FT\right]$