The maximum value of $F$ which can be applied on the system shown in the figure so that both blocks move together with the same acceleration is ..........

Two blocks $A$ and $B$ of masses $4 \ kg$ and $6 \ kg$ are as shown in the figure. $A$ horizontal force of $12 \ N$ is required to make $A$ slip over $B$. Find the maximum horizontal force $F_B$ that can be applied on $B$ so that both $A$ and $B$ move together. (Take $g=10 \ m \ s^{-2}$) (in $N$)

Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest on a smooth horizontal surface as shown in the figure. If the coefficient of friction between $A$ and $B$ is $0.4$,find the maximum horizontal force $F$ that can be applied to block $A$ such that they move together without separation. (in $, N$)

In the arrangement shown in the figure,the coefficient of friction between the two blocks is $0.5$. The force of friction between the two blocks is (Assume that the $4 \,kg$ block is placed on a smooth horizontal surface.) (Acceleration due to gravity $= 10 \,ms^{-2}$.) (in $\,N$)

$A$ block $A$ of mass $4\, kg$ is placed on another block $B$ of mass $5\, kg$,and the block $B$ rests on a smooth horizontal table. If the minimum force that can be applied on $A$ so that both the blocks move together is $12\, N$,the maximum force that can be applied to $B$ for the blocks to move together will be ....... $N$.

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