Question

In one - dimensional head on collision, the relative velocity of approach before collision is equal to :

• A. relative velocity of separation after collision
• B. $e$ times relative velocity of separation after collision
• C. $1/e$ times relative velocity of separation after collision
• D. sum of the velocities after collision

Answer 1

The correct option is C $1/e$ times relative velocity of separation after collision

Coefficient of restitution is given by,

$e=\frac{\text{velocity of separation along line of impact}}{\text{Velocity of approach line of impact}}$

$\therefore e=\frac{v_2-v_1}{u_1-u_2}$

$\therefore u-1-u_2=\frac{1}{e}(v_2-v_1)$

$\therefore$ option C is correct.