Block $A$ of mass $30\, kg$ is resting on a frictionless floor. Another block $B$ of mass $5\, kg$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.4$ while kinetic friction is $0.3$. If a horizontal force of $175\, N$ is applied to block $B$,then the acceleration of block $A$ will be ........ $m/s^2$ $(g = 10\, m/s^2)$.

$A$ block of mass $1\, kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\, m/s^2$,the frictional force acting on the block is ........ $N$.

$A$ 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:

$A$ 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:

When $F = 2 \, N$,the frictional force between the $5 \, kg$ block and the ground is $.......... \, N$.

Determine the time in which the smaller block reaches the other end of the bigger block as shown in the figure. $(g = 10\ m s^{-2})$.