Elastic Collisions In One Dimension
A moving ball of mass m collides head-on and perfectly elastically with a second identical stationary ball on a smooth horizontal surface. After the collision, what happens to the velocities of the two balls?
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- elastic collisions in one dimension
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
The moving ball stops and the second ball moves with the original velocity
As stated in NCERT Class 11, Chapter 6 (Work, Energy and Power), a perfectly elastic collision conserves both momentum and kinetic energy. For two bodies of equal mass where one is initially at rest, solving these two conservation equations simultaneously shows that the velocities are exchanged. Therefore the incoming ball comes to rest and transfers its entire velocity to the previously stationary ball. The option about moving forward together describes a perfectly inelastic collision, which violates kinetic energy conservation here. The rebound option would require the target to be far more massive, like a wall. The both-at-rest option violates momentum conservation, since the total momentum cannot vanish. A consistency check: momentum before is mv and after is also mv carried entirely by the second ball, and kinetic energy (1/2)mv² is fully transferred, satisfying both conservation laws.
This medium difficulty physics question is from the chapter work, energy and power, covering the topic of elastic collisions in one dimension. It appeared in the 2025 exam.
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