Find the maximum force $F$ (in $N$) which will not cause motion of any of the blocks as shown in the figure.

If force $F$ is increasing with time and at $t = 0, F = 0$,where will slipping first start?

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 $B$.

In the given arrangement,find the maximum value of $F$ for which there is no relative motion between the blocks.

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

$A$ $30 \ kg$ 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 $m \ s^{-2}$)