Elastic Collision In One Dimension

In a one-dimensional elastic collision both momentum and kinetic energy are conserved. A well-known consequence is that when two bodies of equal mass collide head-on and one is initially at rest, they simply exchange velocities. Applying $mu=m{v}_1+m{v}_2$ together with the elastic relation that the relative velocity of approach equals the relative velocity of separation, the equal masses force $v_1=0$ and $v_2=u$. Hence the incoming ball stops and the target ball moves off at 4 m/s. The option 4 m/s wrongly assumes the moving ball passes through unchanged, which would violate momentum balance. The option 2 m/s corresponds to a perfectly inelastic stick-together outcome, not an elastic one. The option -4 m/s implies a rebound off a wall-like mass, not an equal partner. Physically, this clean handover of motion is why a row of identical balls in a Newton's cradle passes a swing from one end through to the other almost perfectly. The result hinges critically on the masses being equal; even a slight mismatch would leave the incoming ball with some residual forward or backward velocity. This is the NCERT equal-mass elastic-collision result. As a check, after impact the total kinetic energy is still $\frac{1}{2}m(4{)}^2$, carried entirely by the second ball, confirming energy conservation.