In 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 of $B$ is $m$. …….. $mg$  is the maximum horizontal force $F$ can be applied to the block $B$ so that two blocks move together ?

The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots . N$. (take $\left.g=10\, {ms}^{-2}\right)$

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

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 $\mu$ In above problem, choose the correct value $(s)$ of F which the blocks $M$ and $m$ remain stationary with respect to $M_0$