Q. If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
A) $PV^{2}T^{2}$
B) $P^{- 1}V^{2}T^{- 2}$
C) $PVT^{2}$
D) $P^{- 1}VT^{2}$
Explanation
Let $F\ \propto P^{x}V^{y}T^{z}$ By substituting the following dimensions: $\lbrack P\rbrack = \left\lbrack ML^{- 1}T^{- 2} \right\rbrack\lbrack V\rbrack = \left\lbrack LT^{- 1} \right\rbrack,\lbrack T\rbrack = \lbrack T\rbrack$ and comparing the dimension of both sides $x = 1,y = 2,z = 2,$ so$\ F = PV^{2}T^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.