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Q.
If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
Physical World, Units and Measurements
Solution:
$\left[F\right]=\left[P^{\alpha}\,V^{\beta}\,T^{\gamma}\right]$
or $\left[M^{1}L^{1}T^{-2}\right]=\left[M^{1}L^{-1}T^{-2}\right]^{\alpha}\left[LT^{-1}\right]^{\beta}\left[T\right]^{\gamma}$
or $\left[M^{1}L^{1}T^{-2}\right]=\left[M^{\alpha}L^{-\alpha+\beta}T^{-2\alpha-\beta+\gamma}\right]$
$\alpha=1;\,-\alpha+\beta=1;\,-2\alpha-\beta+\gamma=-2$
or $\beta=2;\,-2-2+\gamma=-2$
or $\gamma=2$
$\Rightarrow \left[F\right]=\left[PV^{2}T^{2}\right]$