The system shown in the figure is released. Find the accelerations $a_1$ (for the $2 \ kg$ block) and $a_2$ (for the $3 \ kg$ block).

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:

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

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

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$(s)$.

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