Two masses m₁ and m₂ moving with velocities V₁ and V₂ in opposite directions collide elastically and after collision m₁ and m₂ move with velocities V₂ and V₁ respectively. The ratio m₂ m₁ is

Step-by-step solution

By the principle of conservation of linear momentum: m₁ V ₁ + m₂ V ₂ = m₁ V ₁' + m₂ V ₂' Given that the final velocities are V ₁' = V ₂ and V ₂' = V ₁ , we substitute these into the momentum equation: m₁ V ₁ + m₂ V ₂ = m₁ V ₂ + m₂ V ₁ Rearranging the terms yields: m₁ ( V ₁ - V ₂) = m₂ ( V ₁ - V ₂) Since the masses are moving in opposite directions, V ₁ V ₂ , which implies V ₁ - V ₂ 0 . Dividing both sides by ( V ₁ - V ₂) gives: m₁ = m₂ Therefore, the ratio m₂ m₁ = 1.0 . Note: In a perfectly elastic collision in one