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To maintain the position of the center of mass at the same position, the velocity of the center of mass Vcm must be zero. The relation between m₁, m₂, v₁, and v₂ is:

1. Vcm = (m₁v₁ + m₂v₂) / (m₁ + m₂)
2. Vcm = m₁v₁ + m₂v₂
3. Vcm = 0 implies m₁v₁ = -m₂v₂
4. Vcm = m₁v₁ - m₂v₂

Correct answer: Vcm = 0 implies m₁v₁ = -m₂v₂

Solution

For the center of mass to remain stationary (Vcm = 0), the total momentum of the system must be zero. This implies m₁v₁ + m₂v₂ = 0, or equivalently, m₁v₁ = -m₂v₂.

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