$A$ block of mass $m$ is placed on the top of another block of mass $M$ as shown in the figure. The coefficient of friction between them is $\mu$. What is the maximum acceleration with which the block $M$ may move so that $m$ also moves along with it?

$A$ pen of mass $m$ is lying on a piece of paper of mass $M$ placed on a rough table. If the coefficients of friction between the pen and paper and the paper and the table are $\mu_1$ and $\mu_2$,respectively,then the minimum horizontal force with which the paper has to be pulled for the pen to start slipping is given by:

Block $A$ weighing $100 \, kg$ rests on a block $B$ and is tied with a horizontal string to the wall at $C$. Block $B$ weighs $200 \, kg$. The coefficient of friction between $A$ and $B$ is $0.25$ and between $B$ and the surface is $1/3$. The horizontal force $P$ necessary to move the block $B$ should be ........ $N$ $(g = 10 \, m/s^2)$.

Two blocks of masses $M$ and $m$ are placed on one another on a smooth horizontal surface as shown in the figure. The force $F$ is acting on the mass $M$ horizontally during time interval $t$. Assuming no relative sliding between the blocks,the work done by friction on the blocks 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 $m \ s^{-2}$)

$A$ block $A$ of mass $4\, kg$ is placed on another block $B$ of mass $5\, kg$,and the block $B$ rests on a smooth horizontal table. If the minimum force that can be applied on $A$ so that both the blocks move together is $12\, N$,the maximum force that can be applied to $B$ for the blocks to move together will be ....... $N$.