Question

If velocity (V), force (F), and energy (E) are taken as fundamental units, then find the dimensional formula for mass.

Answer 1

Let $\left[{ML}^0{T}^0\right]=V^a{F}^b{E}^c$

$=\left[{\left({LT}^{-1}\right)}^a{\left({MLT}^{-2}\right)}^b{\left({ML}^2{T}^{-2}\right)}^c\right]$

Comparing dimensional formula

$b+c=1$

$a+b+2c=0$

$-a-2b-2c=0$ $\Rightarrow$ $-a=2(b+c)$ $\Rightarrow$ $a=-2$

$a+1-c+2c=0$ $\Rightarrow$ $a+1+c=0$ $\Rightarrow$ $-2+1+c=0$ or $c=1$

$b=0$ $\therefore$ $\left[{ML}^0{T}^0\right]=\left[V^{-2}{F}^0{E}^1\right]$