Two blocks $A$ and $B$ of masses $6\, kg$ and $3\, kg$ are placed 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. (Take $g = 10\, m/s^2$)

If the acceleration of block $A$ is $2 \, m/s^2$,which is provided by the frictional force from block $B$,then the magnitude of the frictional force applied by block $B$ on block $A$ is ......... $N$.

$A$ block of mass $m_{2}$ is placed on a horizontal table and another block of mass $m_{1}$ is placed on top of it. An increasing horizontal force $F=\alpha t$ is exerted on the upper block, but the lower block never moves as a result. If the coefficient of friction between the blocks is $\mu_{1}$ and that between the lower block and the table is $\mu_{2}$, then what is the maximum possible value of $\mu_{1} / \mu_{2}$?

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The horizontal surface is frictionless. Find the minimum value of the coefficient of friction $\mu$ between the blocks $M$ and $m_0$ such that all three blocks move together.

In the figure,the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and the mass of $B$ is $m$. What is the maximum horizontal force $F$ that can be applied to the block $B$ so that the two blocks move together?

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