A block of mass $20 \mathrm{kg}$ is kept on a rough incline plane. If the angle of repose is $30°$, then what should be the value of $F_{\mathrm{ext}}$, so that the block does not move over the inclined plane?

The coefficient of static friction, ${\mu }_3$ between the block $A$ of mass $2 \mathrm{kg}$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of the block $B$, so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A horizontal force of $10 \mathrm{N}$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is

A block of mass $20 \mathrm{kg}$ is acted upon by a force $F=30 \mathrm{N}$ at an angle $53°$ with the horizontal in a downward direction as shown. The coefficient of friction between the block and the horizontal surface is $0.2$. The friction force acting on the block by the ground is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\mathrm{\theta }$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is

In the arrangement shown in the figure, $5 \mathrm{kg}$ block is placed on a rough table $\left(\mu =0.4\right)$ and a $3 \mathrm{kg}$ mass is connected at one end, then the range of mass $m_n$ for which the system will remain in equilibrium is

Two masses $A$ and $B$ of $10 \mathrm{kg}$ and $5 \mathrm{kg}$, respectively, are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of $A$ with table is $0.2$. The minimum mass of $C$ that may be placed on $A$ to prevent it from moving is,

A block of mass $m$ is at rest relative to the stationary wedge of mass $M$. The coefficient of friction between block and wedge is $\mu$. The wedge is now pulled horizontally with acceleration $a$ as shown in the figure. Then the minimum magnitude of $a$ for the friction between block and wedge to be zero is