Four blocks are arranged on a smooth horizontal surface as shown. The masses of the blocks are given (see the diagram). The coefficient of static friction between the top and the bottom blocks is ${\mu }_s$. What is the maximum value of the horizontal force $F$, applied to one of the bottom blocks as shown, that makes all four blocks move with the same acceleration?

Two blocks of equal masses $\left(M\right)$ are connected by a string and kept on rough horizontal surface as shown in the figure. The coeffieient of friction between the blocks and the surface is $\mu$. If $0<F_1-F_2<2\mu Mg$, then choose the correct statement.

In the arrangement shown in the figure, the wall is smooth and the friction coefficient between the blocks is $\mu =0.1.$ A horizontal force $F=1000 \mathrm{N}$ is applied on the $2 \mathrm{kg}$ block. A study following statements regarding this situation:

(i) The normal interaction force between the blocks is $1000 \mathrm{N}$.
(ii) The friction force between the blocks is zero.
(iii) Both the blocks accelerate downward with acceleration $g \mathrm{m} {\mathrm{s}}^{-2}$.
(iv) Both the blocks remain at rest.
The correct statements are:

A plank of mass $3 \mathrm{m}$ is placed on a rough inclined plane and a man of mass $m$ walks down the board. If the coefficient of friction between the board and inclined plane is $\mu =0.5$, the minimum acceleration of does not slide is:

If the acceleration is towards right the frictional force exerted by wedge on the block will be (coefficient of friction between wedge and block $=\frac{\sqrt{3}}{2})$

A block is resting over a rough horizontal floor. At $t=0$, a time-varying force starts acting on it, the force is described by equation $F=kt$, where $k$ is constant and $t$ is in seconds. Mark the correct statement(s) for this situation.

Consider the figure shown ,a block $A$ of mass $20 \mathrm{kg}$ is placed over a Block $B$ of $50 \mathrm{kg}$ mass. A horizontal force $F$ is acting on Block $A$ which causes an
acceleration of  $3 {\mathrm{ms}}^{-2}$ to A and $2 {\mathrm{ms}}^{-2}$ to $B$,then the correct statement(s) is/are: