Official Correct Choice:
Option D: \( v_1' = v_2 \, , \, v_2' = v_1 \)
Concept:In a perfectly elastic, one-dimensional collision between two objects of identical mass, the objects completely exchange their velocities.
Formula:$$ v_1' = \left( \frac{m_1 - m_2}{m_1 + m_2} \right)v_1 + \left( \frac{2m_2}{m_1 + m_2} \right)v_2 $$
Solution:- Given \( m_1 = m_2 = m \).
- Substitute this into the equation for the first body: $$ v_1' = \left( \frac{m - m}{m + m} \right)v_1 + \left( \frac{2m}{2m} \right)v_2 = (0)v_1 + (1)v_2 = v_2 $$
- Similarly, for the second body, \( v_2' = v_1 \).
- Therefore, they simply swap velocities.
Why other options are incorrect:Options A and B represent a specific subset where one of the bodies is initially at rest. Option C suggests they bounce back with their own reversed velocities, which only happens if they hit a massive immovable wall.
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