Three blocks $A, B$ and $C$ of masses $1 \mathrm{kg}, 2 \mathrm{kg}$ and $3 \mathrm{kg}$ respectively are arranged as shown in the figure. The coefficient of friction between different surfaces are shown in figure. A force of magnitude $20 \mathrm{N}$ acts on block $B$ in horizontal direction. The acceleration of block $A$ is

In the situation shown in figure, for what value of force $F$ (in Newton) sliding between middle and lower block will start? (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two blocks of masses $m_1$ and $m_2$ connected by a string are placed gently over a fixed inclined plane, such that the tension in the connecting string is initially zero. The coefficient of friction between block $m_1$ and inclined plane is ${\mu }_1$; between $m_2$ and the inclined plane is ${\mu }_2$. The tension in the string shall remain zero if

Two blocks of masses $m_1$ and $m_2$ are connected with a massless unstretched spring and placed over a plank moving with an acceleration $a$ as shown in figure. The coefficient of friction between the blocks and platform is $\mu$.

A board of mass $m=11 \mathrm{kg}$ is placed on the floor and a man of mass $M=70 \mathrm{kg}$ is standing on the board as shown (Case-$I$). The coefficient of friction between the board and the floor is $\mu =0.25$. The maximum force that the man can exert on the rope, so that the board does not slip on the floor is

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: