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 $g = 10\, m/s^2$)

$A$ 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 $B$?

Consider the system shown below. $A$ horizontal force $F$ is applied to a block $X$ of mass $8 \,kg$,such that the block $Y$ of mass $2 \,kg$ adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block $X$. The coefficient of friction between the surfaces of blocks $X$ and $Y$ is $0.5$. The minimum value of $F$ is ............ $N$ (take acceleration due to gravity to be $10 \,ms^{-2}$).

The frictional force acting on the $1 \,kg$ block is .................. $N$.

The coefficient of friction between $4 \, kg$ and $5 \, kg$ blocks is $0.2$ and between $5 \, kg$ block and ground is $0.1$ respectively. Choose the correct statements.

The value of $\theta$ is increased gradually from $\theta = 0$. At $\theta = \tan^{-1}(1/2)$,both blocks just start slipping. Then the value of $\mu_2$ is: $(g = 10 \ m/s^2)$