Question

If velocity $v$, force $F$ and energy $E$ are taken as fundmental units, then dimensional formula for mass will be

• A. $v^{-2}{F}^{0}E$
• B. $v^{-2}{F}^{2}E$
• C. $v^{-2}{F}^0{E}^2$
• D. $v{F}^{2}E$

Answer 1

The correct option is A $v^{-2}{F}^{0}E$

Let $\left[m\right]=\left[v^a{F}^b{E}^c\right]$
$\Rightarrow \left[m\right]=\left[v{]}^a\right[F{]}^b[E{]}^c$
$\Rightarrow \left[M{L}^0{T}^0\right]=\left[L{T}^{-1}{]}^a\right[ML{T}^{-2}{]}^b[M{L}^2{T}^{-2}{]}^c$
$\Rightarrow \left[M{L}^0{T}^0\right]=\left[M^{(b+c)}{L}^{(a+b+2c)}{T}^{(-a-2b-2c)}\right]$
Equating the power of dimensions we get
$a=-2,b=0,c=1$
Thus we have $\left[M\right]=\left[v^{-2}{F}^{0}E\right]$