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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

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If the origin of the coordinate frame of reference is chosen at the centre of mass of a system of \( n \) particles, then the sum \( \sum_{i=1}^{n} m_i \mathbf{r}_i \) is equal to:

  1. \( M\mathbf{R} \)
  2. \( \frac{1}{M} \)
  3. \( 0 \)
  4. \( \sum_{i=1}^n m_i \)

Correct answer · Option 3

\( 0 \)

Explanation

Since \( \mathbf{R} = \frac{\sum m_i \mathbf{r}_i}{M} \), if \( \mathbf{R} = 0 \), it follows that \( \sum m_i \mathbf{r}_i = 0 \).

Related questions

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