The frictional force acting on the $1 \,kg$ block is .................. $N$.

Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg \,wt.$) that can be applied to $A$,so that there will be motion of $A$ and $B$ without relative slipping,is

Block $A$ of mass $3 \ kg$ rests on another block $B$ of mass $7 \ kg$. The coefficient of friction between $A$ and $B$ is $0.4$, while the coefficient of friction between $B$ and the horizontal floor on which $B$ rests is $0.55$. Find the force of friction between $A$ and $B$ when a horizontal force of $50 \ N$ is applied on block $B$. (Use $g = 10 \ m/s^2$) (in $N$)

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).

$A$ $30 \ kg$ slab $B$ rests on a frictionless floor as shown in the figure. $A$ $10 \ kg$ block $A$ rests on top of the slab $B$. The coefficients of static and kinetic friction between the block $A$ and the slab $B$ are $0.60$ and $0.40$ respectively. When block $A$ is acted upon by a horizontal force of $100 \ N$ as shown, find the resulting acceleration of the slab $B$. $(g = 9.8 \ m \ s^{-2})$ (in $m \ s^{-2}$)

Two blocks $(A)$ of $2\,kg$ and $(B)$ of $5\,kg$ rest one over the other on a smooth horizontal plane. The coefficient of static and dynamic friction between $(A)$ and $(B)$ is the same and equal to $0.60$. Find the maximum horizontal force that can be applied to $(B)$ such that both $(A)$ and $(B)$ do not have any relative motion. $(g = 10\,m/s^2)$