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Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the centre of mass of particles through a distance d, by what distance would the particle of mass m₂ move so as to keep the centre of mass of particles at the original position?

1. m₂ / m₁ d
2. m₁ / m₁ + m₂
3. m₁ / m₂ d
4. m₁ d

Correct answer: m₁ / m₂ d

Solution

To keep the center of mass stationary, the displacement of m₂ must balance the displacement of m₁. Using the center of mass condition, m₁ * d = m₂ * x, solving for x gives x = (m₁ / m₂) * d.

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