The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots N$. (take $g=10 \, m/s^2$)

$A$ 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........ $N$. $(g = 10\, m/s^2)$

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 $g = 9.8\, m/s^2$]

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

The figure shows a two-block system. $A$ $4 \,kg$ block rests on a smooth horizontal surface,and the upper surface of the $4 \,kg$ block is rough. $A$ block of mass $2 \,kg$ is placed on its upper surface. Given $\mu_s = 0.8$ and $\mu_k = 0.6$ between the two blocks. The acceleration of the upper block with respect to the earth when the $4 \,kg$ mass is pulled by a force of $30 \,N$ is ......... $m/s^2$.

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