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 $N$?

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

Find the maximum force $F$ (in $N$) for which both the blocks will move with the same acceleration.

The figure shows a two-block system. $A$ $4 \,kg$ block rests on a smooth horizontal surface,and the upper surface of the $4 \,kg$ block is rough. $A$ block of mass $2 \,kg$ is placed on its upper surface. Given $\mu_s = 0.8$ and $\mu_k = 0.6$ between the two blocks. The acceleration of the upper block with respect to the earth when the $4 \,kg$ mass is pulled by a force of $30 \,N$ 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 $, N$)

What is the maximum force $F$ that can be applied on block $m_1$,so that both $m_1$ and $m_2$ will move together? There is no friction between $m_1$ and the horizontal table. The coefficient of friction between $m_1$ and $m_2$ is $\mu$.