Question

If pressure $P$ , velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is

• A. $P V^{2} T^{2}$
• B. $P^{- 1} V^{2} T^{- 2}$
• C. $P V T^{2}$
• D. $P^{- 1} V T^{2}$

Answer 1

Answer: (A)

Let $F \propto P^{x}V^{y}T^{z}$
By substituting the following dimensions:
$\left[P\right]=\left[M L^{- 1} T^{- 2}\right],\left[V\right]=\left[L T^{- 1}\right],\left[T\right]=\left[T\right]$
And comparing the dimension of both sides $x=1,y=2,z=2,$
So $F=PV^{2}T^{2}$