Question

Consider the following statements A and B and identify the correct answer:
$A:$ In an elastic collision, if a body suffers a head on collision with another of same mass at rest, the first body comes to rest while the other starts moving with the velocity of the first one.
$B:$ Two bodies of equal masses suffering a head-on elastic collision merely exchanges their velocities.

• A. A and B are true
• B. A and B are false
• C. A is true but B is false
• D. A is false but B is true

Answer 1

Answer: (A)

A and B are true

For an elastic collision $($ using momentum conservation and coefficient of restitiution $)$,

$v_1=\frac{m_1-m_2}{m_1+m_2}u$

$v_2=\frac{2m_1}{m_1+m_2}u$.

If $m_1=m_2,$ then$,v_1=0,v_2=u$.
In general, the velocities of the bodies just get interchanged in an elastic collision if their masses are equal.