The acceleration of the $10\, kg$ block when $F = 30\, N$ is applied as shown in the figure is ........ $m/s^2$.

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 $N$)

Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest on a smooth horizontal surface as shown in the figure. If the coefficient of friction between $A$ and $B$ is $0.4$,find the maximum horizontal force $F$ that can be applied to block $A$ such that they move together without separation. (in $, N$)

Find the maximum force $F$ (in $N$) for which both the blocks will move with the same acceleration.

The acceleration of block $A$ varies with time as shown in the figure. Find the value of the coefficient of kinetic friction between block $A$ and block $B$.

$A$ body $B$ lies on a smooth horizontal table and another body $A$ is placed on $B$. The coefficient of friction between $A$ and $B$ is $\mu$. What acceleration given to $B$ will cause slipping to occur between $A$ and $B$?