\[\begin {array} {1 1} (a)\;\frac{7}{5} \mu mg & \quad (b)\;\frac{4}{7} \mu mg \\ (c)\;\frac{5}{7} \mu mg & \quad (d)\;\frac{7}{2} \mu mg \end {array}\]

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$Ff= Macm$--------(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$

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