When $F = 2 \text{ N}$,the frictional force between the $10 \text{ kg}$ block and the $5 \text{ kg}$ block is ...... $\text{ N}$. (Assume $g = 10 \text{ m/s}^2$)

$A$ block of mass $m_{2}$ is placed on a horizontal table and another block of mass $m_{1}$ is placed on top of it. An increasing horizontal force $F=\alpha t$ is exerted on the upper block, but the lower block never moves as a result. If the coefficient of friction between the blocks is $\mu_{1}$ and that between the lower block and the table is $\mu_{2}$, then what is the maximum possible value of $\mu_{1} / \mu_{2}$?

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

The maximum value of $F$ which can be applied on the system shown in the figure so that both blocks move together with the same acceleration is ..........

Consider a system of two masses and a pulley shown in the figure. The coefficient of friction between the two blocks and also between the bottom block and the table is $\mu = 0.1$. Find the force $F$ that must be applied to the $0.8 \text{ kg}$ block such that it attains an acceleration of $5 \text{ m/s}^2$. (Assume acceleration due to gravity, $g = 10 \text{ m/s}^2$.) (in $\text{ N}$)

Two blocks ($m = 0.5\, kg$ and $M = 4.5\, kg$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Find the maximum horizontal force $F$ that can be applied on the larger block so that the blocks move together. (Round off to the nearest integer) [Take $g = 9.8\, m/s^2$]