Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Find the value$(s)$ of $F$ for which $M$ and $m$ are stationary with respect to $M_0$.

The rear side of a truck is open and a box of $40 \;kg$ mass is placed $5 \;m$ away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road,the truck starts from rest and accelerates with $2 \;m s^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

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 $10 \,ms^{-2}$).

When $F = 2 \text{ N}$,the frictional force between the $10 \text{ kg}$ block and the $5 \text{ kg}$ block is ...... $\text{ N}$. (Assume $g = 10 \text{ m/s}^2$)

$A$ 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 $B$?

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