A smooth sphere $A$ of mass $m$ collides elastically with an identical sphere $B$ at rest. The velocity of $A$ before collision is $10 \mathrm{m}/\mathrm{s}$ in a direction making $60°$ with the line of centres at the time of impact.

A particle of mass $m$ makes an elastic head-on collision with a stationary particle of mass $2m.$ If initial kinetic energy is moving particle is $6 \mathrm{J}$, then during the impact,

The diagram shows a string of equally placed beads of mass $m$, separated by distance $d$. The beads are free to slide without friction on a thin wire. A constant force $F$ acts on the first bead initially at rest till it makes collision with the second bead. The second bead then collides with the third and so on. Suppose that all collisions are elastic.

Two masses $A$ and $B$ of $3 \mathrm{kg}$ and $2 \mathrm{kg}$ are connected by a long inextensible string which passes over a massless and frictionless pulley. Initially the height of both the masses from the ground is same and equal to $1$ metre. When the masses are released, mass $A$ hits the ground and gets stuck to the ground. Consider the length of the string as large, so that the pulley does not obstruct the motion of masses $A$ and $B. \left[g=10 \mathrm{m}/{\mathrm{s}}^2\right]$