A chain lying on an absolutely smooth table, half of it hanging over the edge of the table as shown in figure $(a)$. The time it takes to slip off the table is affected if two equal weights be attached, one to each end as shown in figure $(b)$ .
$t_a$ : time taken to slip in situation $'a'$
$t_b$ : time taken to slip in situation $'b'$

Block $A$ of mass $4 \;kg$ is to be kept at rest against a smooth vertical wall by applying a force $F$ as shown in figure. The force required is .......... $N$ $\left(g=10 m / s ^2\right)$

Explain main type of force with suitable example.

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $M / 2$. If a force $2 Mg$ is applied at one end of the rope, the force which the rope exerts on the block is -

A football of radius $R$ is kept on a hole of radius $r (r < R)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $\theta$ from the horizontal as shown in the figure below. The maximum value of $\theta$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) -

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.