Question

Consider the following statements $A$ and $B$. Identify the correct choice in the given answers.
A. In a one dimensional perfectly elastic collision between two moving bodies of equal masses, the bodies merely exchange their velocities after collision.
B. If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity, then after collision both travel with same velocity.

• A. $A$ and $B$ are correct
• B. Both $A$ and $B$ are wrong
• C. $A$ is correct, $B$ is wrong
• D. $A$ is wrong, $B$ is correct

Answer 1

Answer: (C)

$A$ is correct, $B$ is wrong

For $A$:
Using the laws of conservation of linear momentum and energy, the velocities of two bodies after perfectly elastic collision are given by
$v_1=\frac{(m_1-m_2)u_1}{m_1+m_2}+\frac{2m_2{u}_2}{m_1+m_2}...\left(i\right)$
$v_2=\frac{2m_1{u}_1}{m_1+m_2}+\frac{(m_2-m_1)u_2}{m_1+m_2}....\left(ii\right)$
where $m_1$ and $m_2$ are the masses of two bodies and $u_1$ and $u_2$ are the velocities of two bodies before collision.
If $m_1=m_2$, then
From (i) and (ii), we get
$v_1=u_2$ and $v_2=u_1$
i.e., in perfectly elastic collision of two moving bodies of equal masses, the bodies merely exchange their velocities after collision. Thus, statement $A$ is correct.
For $B$:
In Eqs. (i) and (ii),
If $m_2<<m_1$ and $u_2=0$, then
$v_1=u_1$ and $v_2=2u_1$
Thus, statement $B$ is wrong.