Block $A$ of mass $100 \ kg$ is kept above another block $B$ of mass $300 \ kg$. Block $A$ is tied to the wall $C$ with a horizontal string. The coefficient of friction between $A$ and $B$ is $0.35$ and that between $B$ and the horizontal surface is $0.5$. Find the horizontal force $P$ necessary to move the block $B$. (in $N$)

$A$ $40 \,kg$ slab rests on a frictionless floor as shown in the figure. $A$ $10 \,kg$ block rests on the top of the slab. The static coefficient of friction between the block and slab is $0.60$ while the kinetic friction is $0.40$. The $10 \,kg$ block is acted upon by a horizontal force $100 \,N$. If $g = 9.8 \,m/s^2$,the resulting acceleration of the slab will be ........ $m/s^2$.

In the figure,the coefficient of friction between the floor and block $B$ is $\mu_1 = 0.2$ and between blocks $A$ and $B$ is $\mu_2 = 0.3$. The masses are $m_A = 20 \text{ kg}$ and $m_B = 40 \text{ kg}$. Find the maximum horizontal force $F$ that can be applied to block $B$ so that both blocks move together. (in $\text{ N}$)

The rear side of a truck is open and a box of $40 \;kg$ mass is placed $5 \;m$ away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road,the truck starts from rest and accelerates with $2 \;m s^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

Initially,the whole system is at rest. Now,a force of $62 \ N$ is applied on block $B$ as shown in the figure. Find the time taken by block $A$ to fall off block $B$.

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: