$N$ number of balls,each of mass $m \ kg$,moving along the positive direction of the $x$-axis,strike a wall per second and return elastically. The velocity of each ball is $u \ m/s$. The force exerted on the wall by the balls in newtons is:

$A$ ball of mass $150\,g$ starts moving with an acceleration of $20\,m/s^2$. When hit by a force,which acts on it for $0.1\,s$. The impulsive force is ........ $N-s$.

$A$ particle moves in the $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{P}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$. If $k$ is a constant,the angle between $\vec{F}$ and $\vec{P}$ will be:

An object with a mass $10 \, kg$ moves at a constant velocity of $10 \, m/s$. $A$ constant force then acts for $4 \, s$ on the object and gives it a speed of $2 \, m/s$ in the opposite direction. The impulse acting on the object is ......... $N \cdot s$.

$100$ balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflect back with the same speed in time $t \ s$. The total magnitude of force exerted by the balls on the wall is

$A$ 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. 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):