$A$ 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 $B$?

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 $\mu$. Identify the correct statement$(s)$.

The blocks are given velocities in the directions shown in the figure. The coefficient of friction between the two blocks is $\mu = 0.5$. Take $g = 10\ m/s^2$. (Consider that the $4\ kg$ block does not fall off the $2\ kg$ block).
Consider the following statements:
$(i)$ Time when relative motion between them stops is $1.4\ s$.
$(ii)$ Time when relative motion between them stops is $1.2\ s$.
$(iii)$ The common velocity of the two blocks is $8\ m/s$,towards the right.
$(iv)$ The displacement of the $4\ kg$ block when relative motion stops is $10.8\ m$.
Which of the statements is/are correct?

$A$ block $A$ of mass $100\, kg$ rests on another block $B$ of mass $200\, kg$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and the ground is $0.3$. The minimum force $F$ required to move the block $B$ is........ $N$. $(g = 10\, m/s^2)$

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

Block $A$ weighing $100 \, kg$ rests on a block $B$ and is tied with a horizontal string to the wall at $C$. Block $B$ weighs $200 \, kg$. The coefficient of friction between $A$ and $B$ is $0.25$ and between $B$ and the surface is $1/3$. The horizontal force $P$ necessary to move the block $B$ should be ........ $N$ $(g = 10 \, m/s^2)$.