\(F=\frac{\alpha-t^2}{\beta v^2}\)

Dimensionally, \(\alpha=\left[ T ^2\right]\)

\(\left[M L T^{-2}\right]=\frac{\left[ T ^2\right]}{\beta\left[L^2 T^{-2}\right]}\)

\(\beta=\frac{ T ^2}{\left[ MLT ^{-2} \cdot L ^2 T ^{-2}\right]}\)

\(\Rightarrow \beta=\left[ M ^{-1} L ^{-3} T ^6\right]\)

Dimensions of \(\frac{\alpha}{\beta}=\frac{ T ^2}{ M ^{-1} L ^{-3} T ^6}=\left[ ML ^3 T ^{-4}\right]\)