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.

Options

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

C

Explanation

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=((m_1+m_2)u_1)/(m_1+m_2)+(2m_2u_2)/(m_1+m_2)`...(i)
`v_2=(2m_1u_1)/(m_1+m_2)+((m_2+m_1)u_2)/(m_1+m_2)`...(ii)
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 (i), If `m_2lt lt m_1` and `u_2= 0`, then `v_1=u_1 and v_2 = 2u_1`
Thus, statement B is wrong.