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 $g = 10\,m/s^2$]

Three blocks $A$,$B$,and $C$ of equal mass $m$ are placed on a smooth surface as shown. The coefficient of friction between any two blocks $A$,$B$,and $C$ is $\mu$. The maximum value of mass $M$ of block $D$ such that blocks $A$,$B$,and $C$ move without slipping over each other is:

As shown in the figure, block $m$ and wedge $M$ move together with a horizontal acceleration of $20\, m/s^2$. Given $m = 1\, kg$, $\mu = 0.6$ (between $m$ and $M$) and $g = 10\, m/s^2$. Choose the $\text{CORRECT}$ alternative:

$A$ $30 \ kg$ 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 $m \ s^{-2}$)

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 $g = 9.8\, m/s^2$]

$A$ 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........ $N$. $(g = 10\, m/s^2)$