NEET2015PhysicsCenter of Mass, Momentum and CollisionActual
Two particles of masses m 1 ,   m 2 move with initial velocities u 1 and u 2 . On collision, one of the particles get excited to higher level, after absorbing energy ε. If final velocities of particles be v 1 and v 2 then we must have:
Options
- Am 1 2 u 1 + m 2 2 u 2 - ε = m 1 2 v 1 + m 2 2 v 2
- B1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 - ε
- C1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 - ε = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2
- D1 2 m 2 u 1 2  +  1 2 m 1 u 1 2 + ε =  1 2 m 2 v 1 2  +

Correct answer
C. 1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 - ε = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2
Step-by-step solution
From conservation of energy initial total energy E i = 1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 After collision total final energy E f = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 + ε ∴ 1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 + ε 1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 - ε = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2