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Two point masses $m$ and $M$ with $M>m$ are placed at two different positions. Where does the centre of mass of this two-body system lie?

1. Closer to the lighter mass $m$
2. Closer to the heavier mass $M$
3. Exactly midway between $m$ and $M$
4. At an arbitrary location unrelated to the masses

Correct answer: Closer to the heavier mass $M$

Solution

The centre of mass is given by the mass-weighted average of positions. Since $M>m$, the weighted average lies nearer to $M$ than to $m$.

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