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

Question

If pressure P , velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is (A) P V2 T2 (B) P- 1 V2 T- 2 (C) P V T2 (D) P- 1 V T2

Tardigrade Admin · Accepted Answer

Let F propto PxVyTz By substituting the following dimensions: [P]=[M L- 1 T- 2],[V]=[L T- 1],[T]=[T] And comparing the dimension of both sides x=1,y=2,z=2, So F=PV2T2

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

$P V^{2} T^{2}$

$P^{- 1} V^{2} T^{- 2}$

$P V T^{2}$

$P^{- 1} V T^{2}$

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

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

PV2T2

P−1V2T−2

PVT2

P−1VT2