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Q.
If force $F$, velocity $v$ and time $T$ are taken as fundamental units. Find the dimension of force in the dimensional formula of pressure.
Physical World, Units and Measurements
Solution:
$\left[F\right]=\left[MLT^{-2}\right]$
$\Rightarrow \left[v\right]=\left[LT^{-1}\right]$
$\therefore \left[L\right]=\left[vT\right]$
$\therefore \left[M\right]=\frac{\left[F\right]}{\left[LT^{-2}\right]}=\frac{\left[F\right]}{\left[vT\right]\times\left[T^{-2}\right]}=\left[Fv^{-1}T\right]$
$\therefore $ Pressure$=\left[ML^{-1}T^{-2}\right]$
$\left[Fv^{-1}T\right]\left[vT\right]^{-1}\left[T^{-2}\right]=\left[Fv^{-2}T^{-2}\right]$
Thus, in the dimensional formula of pressure, the dimension of force is 1.