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

Answer 1

Answer: (B)

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