Question

A teacher gave two statements about coefficient of restitution,
Statement 1: For a perfectly elastic collision $e=1$.
Statement 2: Coefficient of restitution is the ratio of relative velocity of body 2 w.r.t body 1 after collision to relative velocity of body 1 w.r.t body 2 before collision.

Which of the following option is correct?

• A. Statement 1 and statement 2 both are true.
• B. Only statement 1 is true.
• C. Only statement 2 is true.
• D. Statement 1 is true and data is insufficient for statement 2.

Answer 1

The correct option is A Statement 1 and statement 2 both are true.

We know
$e=\frac{\text{relative velocity of separation}}{\text{relative velocity of approach}}=\frac{\text{relative velocity of body 2 w.r.t body 1}}{\text{relative velocity of body 1 w.r.t body 2}}=\frac{v_2-v_1}{u_1-u_2}$

For a perfectly elastic collision;
$u_1-u_2=v_2-v_1$
$\Rightarrow \frac{v_2-v_1}{u_1-u_2}=e=1$

$\therefore$Statement 1 and statement 2 both are true.