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Two particles of masses m₁, m₂ move with initial velocities u₁ and u₂. On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v₁ and v₂ then we must have:

1. 1/2 m₁u₁² + 1/2 m₂u₂² = 1/2 m₁v₁² + 1/2 m₂v₂² − ε
2. 1/2 m₁u₁² + 1/2 m₂u₂² = −1/2 m₁v₁² + 1/2 m₂v₂²
3. −1/2 m₁u₁² + 1/2 m₂u₂² = −1/2 m₁v₁² + 1/2 m₂v₂²
4. m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Correct answer: 1/2 m₁u₁² + 1/2 m₂u₂² = 1/2 m₁v₁² + 1/2 m₂v₂² − ε

Solution

The total initial kinetic energy of the system is reduced by the energy ε absorbed by one particle during excitation. This ensures energy conservation, accounting for the absorbed energy.

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