Match the items in Column-$I$ with those in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Change in momentum	$(a)$ Force
$(2)$ Rate of change of momentum	$(b)$ Impulse

$A$ 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):

Two particles of masses $m_1$ and $m_2$ in projectile motion have velocities $\vec{v}_1$ and $\vec{v}_2$ respectively at time $t = 0$. They collide at time $t_0$. Their velocities become $\vec{v}_1'$ and $\vec{v}_2'$ at time $2t_0$ while still moving in air. The value of $|(m_1\vec{v}_1' + m_2\vec{v}_2') - (m_1\vec{v}_1 + m_2\vec{v}_2)|$ is

Swimming is possible on account of

$A$ body of mass $2 \, kg$ collides with a wall with a speed of $100 \, m/s$ and rebounds with the same speed. If the time of contact was $1/50 \, s$,the force exerted on the wall is:

$A$ block of mass $2\, kg$ is suspended by a string of length $5\, m$. It is released from a horizontal position (as shown in the figure) such that the string is initially slack. What will be the impulse when the string just becomes tight? (Take $g = 10\, m/s^2$)