What is the acceleration of the block and trolley system shown in the figure,if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

$A$ block $A$ with mass $100\, kg$ is resting on another block $B$ of mass $200\, kg$. As shown in the figure,a horizontal rope tied to a wall holds block $A$. The coefficient of friction between $A$ and $B$ is $0.2$,while the coefficient of friction between $B$ and the ground is $0.3$. The minimum required force $F$ to start moving block $B$ will be ........ $N$.

$A$ man of mass $40\, kg$ is standing on a trolley $A$ of mass $140\, kg$. He pushes another trolley $B$ of mass $60\, kg$,so that they are set in motion. Then:

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then identify the correct statement$(s)$ related to the tension $T$ in the string.

In a tug-of-war contest,two men pull on a horizontal rope from opposite sides. The winner will be the man who

Give the magnitude and direction of the net force acting on a stone of mass $0.1\; kg$,
$(a)$ just after it is dropped from the window of a stationary train,
$(b)$ just after it is dropped from the window of a train running at a constant velocity of $36\; km/h$,
$(c)$ just after it is dropped from the window of a train accelerating with $1\; m/s^2$,
$(d)$ lying on the floor of a train which is accelerating with $1\; m/s^2$,the stone being at rest relative to the train.
Neglect air resistance throughout.