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 $B$.

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If friction exists between the block $M$ and the block $m_0$ and there is no friction between the block $M$ and the horizontal surface,then the minimum value of $\mu$ for which the block $m_0$ remains stationary with respect to $M$ is:

The system shown in the figure is released. Find the accelerations $a_1$ (for the $2 \ kg$ block) and $a_2$ (for the $3 \ kg$ block).

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The horizontal surface is frictionless. Find the minimum value of the coefficient of friction $\mu$ between the blocks $M$ and $m_0$ such that all three blocks move together.

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

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