Define force. What is contact force ? Write two example of field force.

A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L\, (L >> r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure) . If one of the beads is now given a speed $v$, the average force experienced by each support after a long time is (assume all collisions are elastic)

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) -

An object of mass $5\, kg$ is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of $10\, N$ throughout the motion. The ratio of time of ascent to the time of descent will be equal to $\left[\right.$Use $g =10 \,ms ^{-2}]$

The restoring force of a spring with a block attached to the free end of the spring is represented by

Two masses $m$ and $M$ are attached to the strings as shown in the figure. If the system is in equilibrium, then