Block $A$ of mass $3 \ kg$ rests on another block $B$ of mass $7 \ kg$. The coefficient of friction between $A$ and $B$ is $0.4$, while the coefficient of friction between $B$ and the horizontal floor on which $B$ rests is $0.55$. Find the force of friction between $A$ and $B$ when a horizontal force of $50 \ N$ is applied on block $B$. (Use $g = 10 \ m/s^2$) (in $N$)

Block $A$ of mass $2 \, kg$ is placed over block $B$ of mass $8 \, kg$. The combination is placed over a rough horizontal surface. The coefficient of friction between block $B$ and the floor is $0.5$. The coefficient of friction between blocks $A$ and $B$ is $0.4$. A horizontal force of $10 \, N$ is applied on block $B$. Find the force of friction between blocks $A$ and $B$. (Take $g = 10 \, ms^{-2}$)

Two blocks $A$ and $B$ of masses $m_A = 1\,kg$ and $m_B = 3\,kg$ are kept on a table as shown in the figure. The coefficient of friction between $A$ and $B$ is $\mu_1 = 0.2$ and between $B$ and the surface of the table is $\mu_2 = 0.2$. The maximum horizontal force $F$ that can be applied on $B$ such that block $A$ does not slide over block $B$ is ........ $N$. [Take $g = 10\,m/s^2$]

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.

The maximum value of $F$ which can be applied on the system shown in the figure so that both blocks move together with the same acceleration is ..........

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?