The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots N$. (take $g=10 \, m/s^2$)

Block $A$ of mass $30\, kg$ is resting on a frictionless floor. Another block $B$ of mass $5\, kg$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.4$ while kinetic friction is $0.3$. If a horizontal force of $175\, N$ is applied to block $B$,then the acceleration of block $A$ will be ........ $m/s^2$ $(g = 10\, m/s^2)$.

If $100 \,N$ force is applied to $10 \,kg$ block as shown in the diagram,the acceleration of $40 \,kg$ slab is (in $\,ms^{-2}$)

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The horizontal surface is frictionless. Find the minimum value of the coefficient of friction $\mu$ between the blocks $M$ and $m_0$ such that all three blocks move together.

When $F = 2\,N$,the frictional force between the $10\,kg$ block and the $5\,kg$ block is $..........\,N$. (Given: $\mu_s = 0.1$ between blocks,$\mu_s = 0.3$ between $5\,kg$ block and ground).

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: