After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2m$ at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body $A$ is:

$A$ neutron travelling with a velocity $v$ and kinetic energy $E$ collides perfectly elastically head-on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by the neutron is

$A$ particle of mass $m$ moving with a velocity $u$ makes an elastic one-dimensional collision with a stationary particle of mass $m$. They are in contact for a total time $T$. The contact force increases linearly from $0$ to $F_0$ in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$, and decreases linearly from $F_0$ to $0$ in the final time $\frac{T}{4}$, as shown in the graph. The magnitude of $F_0$ is:

When does the maximum energy transfer occur during an elastic collision?

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.