Question

If force $F$, velocity $v$ and time $T$ are taken as fundamental units. Find the dimension of force in the dimensional formula of pressure.

• A. $3$
• B. $5$
• C. $6$
• D. $1$

Answer 1

Answer: (D)

$\left[F\right]=\left[ML{T}^{-2}\right]$

$\Rightarrow \left[v\right]=\left[L{T}^{-1}\right]$

$\therefore \left[L\right]=\left[vT\right]$

$\therefore \left[M\right]=\frac{\left[F\right]}{\left[L{T}^{-2}\right]}=\frac{\left[F\right]}{\left[vT\right]\times \left[T^{-2}\right]}=\left[F{v}^{-1}T\right]$

$\therefore$ Pressure$=\left[M{L}^{-1}{T}^{-2}\right]$

$\left[F{v}^{-1}T\right]{\left[vT\right]}^{-1}\left[T^{-2}\right]=\left[F{v}^{-2}{T}^{-2}\right]$

Thus, in the dimensional formula of pressure, the dimension of force is 1.