With what minimum acceleration mass $M$ be moved on a frictionless surface so that m remains stuck to it as shown in Fig.E5.30. The coefficient of friction between $M$ and m is $\mu .$

Free Body diagram of 'm' Mass.

$N=$ Normal force due to $\text{'}M’$ mass.

$f=$ friction force $\Rightarrow {\mu }_N=f$

Balancing force in Horizontal Direction:

$N=ma\to \left(1\right)$

Balancing force in vertical Direction:

$f=mg$

for Limiting case and stucking of ‘m’ mass with $‘N’$ Mass:

$$\begin{gathered} f_{min}\ge mg \\ {\mu }_N\ge mg \\ {\mu }_{ma}=mg \\ a=\frac{g}{\mu }m/se{c}^2 \end{gathered}$$

So, minimum acceleration of ‘M’ mass should be $a=\frac{g}{\mu }m/se{c}^2$