Select the incorrect statement for the given situation: Two bodies with mass m₁ and m₂ undergo elastic collision

The correct option is: "When m₁ > m₂, m2 will move with four times increase in its velocity than m₁"

Let us analyze the physics of a one-dimensional elastic collision to understand why this statement is incorrect (and thus the correct choice for this question), while examining the behavior of the system.

Consider a body of mass $m_1$ moving with an initial velocity $u_1$ which undergoes a head-on elastic collision with a body of mass $m_2$ initially at rest ($u_2=0$).

Using the conservation of linear momentum and the conservation of kinetic energy, the final velocities $v_1$ and $v_2$ of the two bodies after the collision are given by the standard relations:

$v_1=\frac{m_1-m_2}{m_1+m_2}{u}_1$

$v_2=\frac{2m_1}{m_1+m_2}{u}_1$

Let us evaluate the limiting case where the mass of the colliding body is extremely large compared to the target body, i.e., $m_1\gg m_2$ (so $m_2\to 0$):

$v_1\approx \frac{m_1}{m_1}$

$v_2\approx \frac{2m_1}{m_1}$

In this extreme limit, the heavier body $m_1$ continues to move with virtually its original velocity $u_1$, whereas the lighter body $m_2$ is set into motion with approximately twice the velocity of $m_1$ (an increase to $2v_1$).

Since the maximum possible velocity that $m_2$ can acquire under these conditions is only twice that of $m_1$, the statement asserting that $m_2$ will move with a four-fold increase in velocity relative to $m_1$ is physically incorrect. Thus, it is the incorrect statement representing the correct choice.