$Ff= Macm$--------(1)
$f_e= I \alpha$
$f= \large\frac{2}{5}$$ MR^2.\large \frac{\alpha}{R}$
$f= \large\frac{2}{5} Ma _{cm}$------(2)[$ a_{cm}=Rd$ for rolling]
$\mu mg \geq \large\frac{2}{5} $$m a_{cm}$
$a_{cm} \leq \large\frac{5}{2}$$ \mu g$
From (1) and (2)
$F= M \bigg[ 1+ \large\frac{2}{5} \bigg]a_{cm}$
$\quad= \large\frac{7}{5}$$ M a_{cm}$
$F_{max }= \large\frac{7}{5}$$ M \large\frac{5}{2}$$\mu g$
$\qquad= \large\frac{7}{2}$$ M \mu g$