$A$ 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 $\dots \; N$.

Two blocks ($m = 0.5\, kg$ and $M = 4.5\, kg$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Find the maximum horizontal force $F$ that can be applied on the larger block so that the blocks move together. (Round off to the nearest integer) [Take $g = 9.8\, m/s^2$]

$A$ block $A$ of mass $100\, kg$ rests on another block $B$ of mass $200\, kg$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and the ground is $0.3$. The minimum force $F$ required to move the block $B$ is........ $N$. $(g = 10\, m/s^2)$

When $F = 2 \, N$,the frictional force between the $5 \, kg$ block and the ground is $.......... \, N$.

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

$A$ $40 \,kg$ 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 ........ $m/s^2$.