Physics - Unit & Dimension Question with Solution | TestHub

Let $E^a{v}^b{F}^c=[M]$.Then
${\left(\left[M{L}^2{T}^{-2}\right]\right)}^a{\left(\left[L{T}^{-1}\right]\right)}^b{\left(\left[ML{T}^{-2}\right]\right)}^c=[M]$ gives
$a+c=1,2a+b+c=0$
, $-2a-b-2c=0$
, so $a=1,b=-2,c=0$ : mass
$=\left[E{v}^{-2}\right]$.