The velocity, acceleration and force in two systems of units are related as under
(i) $v^{\text{'}}=\frac{{\alpha }^2}{\beta }v$     (ii) $a^{\text{'}}=\left(\alpha \beta \right)a$     (iii)  $F^{\text{'}}=\left(\frac{1}{\alpha \beta }\right)F$  
All the primed symbols belong to one system and unprimed ones belong to the other system.  $\alpha$ and $\beta$ are dimensionless constants.  Which of the following is/are correct?

$$\begin{gathered} Velocity = length time, acceleration=length{\left(time\right)}^2 \\ \Rightarrow Length=\frac{{\left(Velocity\right)}^2}{acceleration}i.e,L^{\text{'}}=\frac{v^{\text{'}2}}{a^{\text{'}}},L=\frac{v^2}{a} \\ \Rightarrow \frac{L^{\text{'}}}{L}={\left(\frac{v^{\text{'}}}{v}\right)}^2\left(\frac{a}{a^{\text{'}}}\right)=\left(\frac{{\alpha }^2}{\beta }\right)\frac{1}{\alpha \beta }={\alpha }^3/{\beta }^3 \\ Now, m^{\text{'}}=\frac{F^{\text{'}}}{a^{\text{'}}},m=\frac{F}{a} \\ \frac{m^{\text{'}}}{m}=\frac{F^{\text{'}}}{F}\frac{a}{a^{\text{'}}}=\frac{1}{\alpha \beta }\times \frac{1}{\alpha \beta }=\frac{1}{{\alpha }^2{\beta }^2} \end{gathered}$$

Time = velocity/acceleration, i.e.,

$$\begin{gathered} T^{\text{'}}=\frac{v^{\text{'}}}{a^{\text{'}}} and T=\frac{v}{a} \\ \frac{T^{\text{'}}}{T}=\frac{v^{\text{'}}}{v}\frac{a}{a^{\text{'}}}=\frac{{\alpha }^2}{\beta }\frac{1}{\alpha \beta }=\frac{\alpha }{{\beta }^2} \end{gathered}$$

$Momentum = mass \times velocity$

$p^{\text{'}}=m^{\text{'}}{v}^{\text{'}},P=mv,\frac{p^{\text{'}}}{p}=\frac{m^{\text{'}}}{m}\frac{v^{,}}{v}=\frac{1}{{\alpha }^2{\beta }^2}\frac{{\alpha }^2}{\beta }\frac{{\alpha }^2}{\beta }=\frac{1}{{\beta }^4}$