Physics - Unit & Dimension Question with Solution | TestHub

$\left[M\right]=\left[\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}\right]=\left[M^0{L}^0{T}^0\right]$
$\left[J\right]=\left[\mathrm{A}\mathrm{n}\mathrm{g}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{m}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{m}\right]=\left[M{L}^2{T}^{-1}\right]$
$\left[L\right]=\left[\mathrm{L}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\right]$
[Now as angular momentum is dimensionless]
$\left[M{L}^2{T}^{-1}\right]=\left[M^0{L}^0{T}^0\right]$
$\therefore \left[L^2\right]=\left[T\right]$
$\therefore \mathrm{P}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\left[P\right]=\left[ML{T}^{-2}\cdot L{T}^{-1}\right]$$\left(asP=F\cdot V\right)$
$=\left[M{L}^2{T}^{-3}\right]$
$=\left[L^2{L}^{-6}\right]$
$\Rightarrow \left[P\right]=\left[L^{-4}\right]\Rightarrow \left(\mathrm{A}\right)$is incorrect.
Energy/Work$\left[W\right]=\left[ML{T}^{-2}\cdot L\right]$(using,$\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}=\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\times \mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}$
$=\left[L^2{L}^{-4}\right]$
$=\left[L^{-2}\right]\Rightarrow \left(\mathrm{D}\right)$is correct.
$\mathrm{F}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}\left[F\right]=\left[ML{T}^{-2}\right]=\left[L\cdot L^{-4}\right]=\left[L^{-3}\right]\Rightarrow \left(\mathrm{B}\right)$is correct.
Linear momentum$\left[P\right]=\left[ML{T}^{-1}\right]=\left[L\cdot L^{-2}\right]$
$\left[p\right]=\left[L^{-1}\right]\Rightarrow \left(\mathrm{C}\right)$is correct.