Question

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

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

Answer 1

The correct option is C $A{v}^2\rho$

According to question,
$F\alpha A^2{v}^2{\rho }^2$
$F=k{A}^2{v}^2{\rho }^2$
Dimension of force $F=\left[M^1{L}^1{T}^{-2}\right]$
Dimension of area $A=\left[M^0{L}^2{T}^0\right]$
Dimension of velocity $v=\left[L^1{T}^{-1}\right]$
Dimension of density $\rho =\left[M{L}^{-3}\right]$
$\Rightarrow ML{T}^{-2}=\left[L^2{]}^x\right[L{T}^{-1}{]}^y[M{L}^{-3^{}}{]}^z$