Two blocks $A$ and $B$ of masses $4 \ kg$ and $6 \ kg$ are as shown in the figure. $A$ horizontal force of $12 \ N$ is required to make $A$ slip over $B$. Find the maximum horizontal force $F_B$ that can be applied on $B$ so that both $A$ and $B$ move together. (Take $g=10 \ m \ s^{-2}$) (in $N$)

The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots N$. (take $g=10 \, m/s^2$)

$A$ force of $0.5 \ N$ is applied on the upper block as shown in the figure. The coefficient of static friction between the two blocks is $0.1$ and that between the lower block and the surface is zero. The work done by the lower block on the upper block for a displacement of $3 \ m$ of the upper block is ...... $J$.

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

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

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Find the value$(s)$ of $F$ for which $M$ and $m$ are stationary with respect to $M_0$.