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

Asked in NEET 2015 · Energy balance in inelastic collisions

• (1) 1/2m₁u₁²+1/2m₂u₂²-ε=1/2m₁v₁²+1/2m₂v₂²
• (2) 1/2m₁²u₁²+1/2m₂²u₂²+ε=1/2m₁²v₁²+1/2m₂²v₂²
• (3) m₁²u₁+m₂²u₂-ε=m₁²v₁+m₂²v₂
• (4) 1/2m₁u₁²+1/2m₂u₂²=1/2m₁v₁²+1/2m₂v₂²-ε

Step-by-step solution

Why the other options are wrong

• (2) Squares the masses and puts ε on the wrong side of the balance.
• (3) Squares the masses and uses the velocities to the first power — not an energy equation at all.
• (4) Rearranges to make the final kinetic energy larger than the initial by ε, which would mean the excitation gave energy back rather than took it.

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