Physics - Unit & Dimension Question with Solution | TestHub

Let$M\propto \left[F^a{L}^b{T}^c\right]$

Writing dimensions on both sides and using the principle of homogeneity of dimensions we have,

$\left[M^1{L}^0{T}^0\right]=k{\left[ML{T}^{-2}\right]}^a{\left[L\right]}^b{\left[T\right]}^c$

On comparing the power on both sides we get$a=1,a+b=0$and$-2a+c=0$

On solving we have$b=-1,c=2,a=1$

$\therefore$units of mass is$\left[F{L}^{-1}{T}^2\right]$