Two blocks $A$ and $B$ of masses $2 \ kg$ and $4 \ kg$ respectively are kept on a rough horizontal surface. If the same force of $20 \ N$ is applied on each block,then the ratio of the accelerations of the blocks $A$ and $B$ is (Coefficient of kinetic friction between the surface and the blocks is $0.3$ and acceleration due to gravity $= 10 \ m \ s^{-2}$).

$A$ uniform rod of length $L$ and mass $M$ is placed on a rough horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod such that the rod is just in the state of rest. The coefficient of friction varies according to the relation $\mu = Kx$,where $K$ is a positive constant and $x$ is the distance from the end where the force is not applied. Find the tension at the midpoint of the rod.

$A$ wooden block of mass $M$ resting on a rough horizontal surface is pulled with a force $F$ at an angle $\phi$ with the horizontal. If $\mu$ is the coefficient of kinetic friction between the block and the surface,then the acceleration of the block is:

$A$ cylinder of mass $10\,kg$ is sliding on a plane with an initial velocity of $10\,m/s$. If the coefficient of friction between the surface and the cylinder is $0.5$,then before stopping,it will travel a distance of ............. $m$.

$A$ block of mass $2 \,kg$ is being pushed against a wall by a force $F=90 \,N$ as shown in the figure. If the coefficient of friction is $0.25$, then the magnitude of acceleration of the block is (Take $g=10 \,ms^{-2}$, $\sin 37^{\circ}=\frac{3}{5}$). (in $\,ms^{-2}$)

Determine the maximum acceleration in $m/s^2$ of the train in which a box lying on its floor will remain stationary,given that the coefficient of static friction between the box and the train's floor is $0.15$.