Consider the diagram shown below in which two masses of $m$ and $2m$ are placed on a fixed triangular wedge. The coefficient of friction between block $A$ (mass $m$) and the wedge is $\mu_A = 2/3$,while that for block $B$ (mass $2m$) and the wedge is $\mu_B = 1/3$. Find the acceleration of the system.

$A$ small block of mass $0.1 \ kg$ lies on a fixed inclined plane $PQ$ which makes an angle $\theta$ with the horizontal. $A$ horizontal force of $1 \ N$ acts on the block through its center of mass as shown in the figure. The block remains stationary if (take $g = 10 \ m/s^2$):

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

An object of mass $M$ is placed on a rough horizontal surface (coefficient of friction $\mu$). $A$ person tries to pull the object by applying a horizontal force,but the object does not move. The force $F$ exerted by the surface on the object is:

Three weights $A, B$ and $C$ are connected by strings as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is acceleration due to gravity):

$A$ car accelerates on a horizontal road due to the forces exerted by