Question

If area $\left(A\right)$ velocity $\left(v\right)$ and density $\left(p\right)$ are base units, then the dimensional formula of force can be represented as.

• A. $Av\rho$
• B. $A{v}^2\rho$
• C. $Av{\rho }^2$
• D. $A^{2}v\rho$

Answer 1

Answer: (B)

$F=k{A}^x{v}^y{\rho }^z$
$\Rightarrow ML{T}^{-2}={\left[L^2\right]}^x{\left[L{T}^1\right]}^y{\left[M{L}^{-3}\right]}^z$
$\Rightarrow z=1,2x+y-3z=1,y=-2$
$\Rightarrow y=2$
$\Rightarrow x=1$
$F=k{A}^1{v}^2{\rho }^1$
$=A{v}^2\rho ,k=1$