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 book is lying on the table. What is the angle between the action of the book on the table and the reaction of the table on the book?

A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?

Which of the following groups of forces could be in equibrium

A car of mass $m$ when passes over top of convex bridge of radius of curvature $r,$ with a velocity $v,$ then the normal force exerted by the bridge on the car is 

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.