Find the acceleration of the $10\,kg$ block when a force $F = 30\,N$ is applied as shown in the figure. The coefficients of friction are $\mu = 0.1$ between the blocks and $\mu = 0.3$ between the $5\,kg$ block and the ground. (in $,m/s^2$)

$A$ 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.

If the acceleration of block $A$ is $2 \, m/s^2$,which is provided by the frictional force from block $B$,then the magnitude of the frictional force applied by block $B$ on block $A$ is ......... $N$.

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 $10\,kg$ block and the $5\,kg$ block is $..........\,N$. (Given: $\mu_s = 0.1$ between blocks,$\mu_s = 0.3$ between $5\,kg$ block and ground).

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