Determine the time in which the smaller block reaches the other end of the bigger block as shown in the figure. $(g = 10\ m s^{-2})$.

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

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?

The coefficient of friction between $4 \, kg$ and $5 \, kg$ blocks is $0.2$ and between $5 \, kg$ block and ground is $0.1$ respectively. Choose the correct statements.

$A$ 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?

$A$ $30 \ kg$ slab $B$ rests on a frictionless floor as shown in the figure. $A$ $10 \ kg$ block $A$ rests on top of the slab $B$. The coefficients of static and kinetic friction between the block $A$ and the slab $B$ are $0.60$ and $0.40$ respectively. When block $A$ is acted upon by a horizontal force of $100 \ N$ as shown, find the resulting acceleration of the slab $B$. $(g = 9.8 \ m \ s^{-2})$ (in $m \ s^{-2}$)