Question

Two small, identical steel balls collide completely elastically. Initially, ball 1 is moving with velocity v1 directly toward ball 2, and ball 2 is stationary. After the collision, the final velocities of ball 1 and ball 2 are, respectively

A) v1 / 2; v1 / 2

B) v1; 2v1

C) -v1; 2v1

D) 0; v1

E) -v1; 0

Answer 1

Elastic collision means both conservation of momentum and conservation of energy is obeyed

Momentum before collision = momentum after collision

\(\mathrm{Mv}_{1 \mathrm{~b}}+0=\mathrm{Mv}_{1 \mathrm{a}}+\mathrm{Mv}_{2 \mathrm{a}}\)

\(\mathrm{v}_{1 \mathrm{~b}}=\mathrm{v}_{1 \mathrm{a}}+\mathrm{v}_{2 \mathrm{a}}\)

From the options the possibilities that conserve momentum are option \(\mathrm{A}\), option \(\mathrm{C}\) and option D but only option D obeys conservation of energy

$$ \frac{M v_{1}^{2}}{2}+0=0+\frac{M v_{1}^{2}}{2} $$

Hence the solution is option \(\mathrm{D}\left(0, \mathrm{v}_{1}\right)\)