Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_{1}$ to $F_{2}$ is $1: x$ where $x =....$

Write condition of translational equilibrium of particle.

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)

Write day to day life example in which motion is controlled.

If an inclined plane is made slowly horizontal by reducing its inclination with horizontal, the component of weight parallel to the plane of block resting on the inclined plane

A weight can be hung in any of following four ways by using same string. In which case is  the string more likely to break is :-