$A$ body $B$ lies on a smooth horizontal table and another body $A$ is placed on $B$. The coefficient of friction between $A$ and $B$ is $\mu$. What acceleration given to $B$ will cause slipping to occur between $A$ and $B$?

$A$ system of two blocks of masses $m = 2 \; kg$ and $M = 8 \; kg$ is placed on a smooth table as shown in the figure. The coefficient of static friction between the two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\dots \; N$.

$A$ $40 \,kg$ slab rests on a frictionless floor as shown in the figure. $A$ $10 \,kg$ block rests on the top of the slab. The static coefficient of friction between the block and slab is $0.60$ while the kinetic friction is $0.40$. The $10 \,kg$ block is acted upon by a horizontal force $100 \,N$. If $g = 9.8 \,m/s^2$,the resulting acceleration of the slab will be ........ $m/s^2$.

Find the maximum force $F$ (in $N$) which will not cause motion of any of the blocks as shown in the figure.

Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between the bottom block and the table is $\mu = 0.1$. Find the force $F$ that must be applied to the $0.8 \text{ kg}$ block such that it attains an acceleration of $5 \text{ m/s}^2$. (Assume acceleration due to gravity, $g = 10 \text{ m/s}^2$.) (in $\text{ N}$)

The acceleration of the $10\, kg$ block when $F = 30\, N$ is applied as shown in the figure is ........ $m/s^2$.