The coefficient of friction between blocks $A$ and $B$ is $\mu$. The minimum force $F$ with which $A$ must be pushed such that $B$ will not slip down is

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 maximum acceleration of the $5\, kg$ block is ...... $m/s^2$.

Two blocks $(A)$ of $2\,kg$ and $(B)$ of $5\,kg$ rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between $(A)$ and $(B)$ is the same and equal to $0.60$. Find the maximum horizontal force that can be applied to $(B)$ such that both $(A)$ and $(B)$ do not have any relative motion. $(g = 10\,m/s^2)$

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 ......... $N$.

Two blocks of masses $M$ and $m$ are placed on one another on a smooth horizontal surface as shown in the figure. The force $F$ is acting on the mass $M$ horizontally during time interval $t$. Assuming no relative sliding between the blocks,the work done by friction on the blocks is .......... .