L, v', A', F' \(\Rightarrow\) \(\frac{1}{kv^{r}A^{r}F^{r}}\)

Putting the dimensions in the above relation

\(\left[ML^{2}T^{-2}\right] = k\left[L T^{-1}\right]^{x}\left[L T^{-2} y\right]\left[ML T^{-2}\right]^{z}\)

⇒ ⇒ \(\left[ M L^{2} T^{-1} \right] = k \left[ M^{2} L^{x+v+2} T^{x} y^{-2} \right]\)

Comparing the powers of M, L and \tau

z = 1 …(i)

x + y + z = 2 … (ii)

-x - 2y - 2z = -1 … (iii)

On solving (i), (ii) and (iii) \(x \quad 3y \quad -2z \quad 1\)

So dimension of l in terms of \nu, A and \(\int\)

\(\left[L\right] = \left[F V^{2} A^{-2}\right]\)