a
From principle of homogeneity
${[F]=\left[\alpha t^2\right]=[\beta t]}$
${[\alpha]=\frac{[F]}{\left[t^2\right]} \text { and }[\beta]=\frac{[F]}{[t]}}$
$\therefore \quad[\alpha][t]=[\beta]$
$\therefore \quad \frac{\alpha t}{\beta}=\text { dimensionless }$