In the given arrangement,find the maximum value of $F$ for which there is no relative motion between the blocks.

$A$ block $A$ of mass $100\, kg$ rests on another block $B$ of mass $200\, kg$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and the ground is $0.3$. The minimum force $F$ required to move the block $B$ is........ $N$. $(g = 10\, m/s^2)$

The coefficient of friction between $4 \, kg$ and $5 \, kg$ blocks is $0.2$ and between $5 \, kg$ block and ground is $0.1$ respectively. Choose the correct statements.

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 $N$)

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

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 $g = 9.8\, m/s^2$]