If area (A), velocity (v) and density (ρ) are base units, then the dimensional formula of force can be represented as
Answer & explanation
Correct answer: option 2
F = $A^av^b\rho^c$
⇒ $[MLT^{-2}]$ = $[L^2]^a[LT^{-1}]^b[ML^{-3}]^c$= $[M^cL^{2a+b-3c}T^{-b}]$
Comparing the coefficient on both sides
c = 1
-b = -2 ⇒ b = 2
2a+b-3c = 1 ⇒ a = 1
F = $Av^2\rho$