$A$ block of mass $m$ is placed on the top of another block of mass $M$ as shown in the figure. The coefficient of friction between them is $\mu$. What is the maximum acceleration with which the block $M$ may move so that $m$ also moves along with it?

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?

Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest 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. (in $, N$)

Two blocks ($m = 0.5\, kg$ and $M = 4.5\, kg$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Find the maximum horizontal force $F$ that can be applied on the larger block so that the blocks move together. (Round off to the nearest integer) [Take $g = 9.8\, m/s^2$]

Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between the bottom block and the table is $\mu = 0.1$. Find the force $F$ that must be applied to the $0.8 \text{ kg}$ block such that it attains an acceleration of $5 \text{ m/s}^2$. (Assume acceleration due to gravity, $g = 10 \text{ m/s}^2$.) (in $\text{ N}$)

The acceleration of the $10\, kg$ block when $F = 30\, N$ is applied as shown in the figure is ........ $m/s^2$.