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.
1. Both A and B are true 2. Both A and B are false
3. A is true but B is false 4. A is false but B is true

Answer 1

We know,
$v_1 = (\frac{m_1-m_2 }{m_1+m_2}) u_1 + (\frac{2m_2}{m_1+m_2})u_2$
$v_2 = (\frac{2m_1 }{m_1+m_2}) u_1 + (\frac{m_2-m_1}{m_1+m_2})u_2$
A. If $u_2 = 0$ and $m_1=m_2$
    $v_2=(\frac{2m}{2m}) u_1$
    $v_2 = u_1$

B. If $m_1=m_2$ then $v_1=u_2$ and $v_2 = u_1$
    Then $v_1=0$
     $v_2=(\frac{2m}{2m}) u_1$
     $v_2 = u_1$
     
So, 1 is right.
Both A and B is true