The coefficient of friction between two blocks is $0.2$,and the coefficient of friction between block $B$ and the surface is $0.5$. If a force of $25 \ N$ is applied to block $B$ (mass $A = 2 \ kg$,mass $B = 8 \ kg$),what is the magnitude of the frictional force between the two blocks in $N$?

In the figure,the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and the mass of $B$ is $m$. What is the maximum horizontal force $F$ that can be applied to the block $B$ so that the two blocks move together?

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

Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest on a smooth horizontal surface as shown in the figure. If the coefficient of friction between $A$ and $B$ is $0.4$,find the maximum horizontal force $F$ that can be applied to block $A$ such that they move together without separation. (in $, N$)

$A$ $40 \,kg$ slab rests on a frictionless floor. $A$ $10 \,kg$ block rests on top of the slab. The coefficient of friction between the block and the slab is $0.40$. The $10 \,kg$ block is acted upon by a horizontal force of $100 \,N$. If $g=10 \,m/s^2$,the resulting acceleration of the slab will be ............. $m/s^2$.

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