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(A) For a system of $n$ particles of equal mass $m$,the position vector of the centre of mass $\vec{R}$ is given by the formula:$\vec{R} = \frac{\sum_

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At the geometric centre

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(A) For a system of $n$ particles of equal mass $m$,the position vector of the centre of mass $\vec{R}$ is given by the formula:$\vec{R} = \frac{\sum_{i=1}^{n} m_i \vec{r}_i}{\sum_{i=1}^{n} m_i}$Since all masses are equal $(m_1 = m_2 = ... = m_n = m)$,the formula simplifies to:$\vec{R} = \frac{m \sum_{i=1}^{n} \vec{r}_i}{nm} = \frac{1}{n} \sum_{i=1}^{n} \vec{r}_i$This expression represents the arithmetic mean of the position vectors of the particles.Therefore,the centre of mass of particles of equal mass is located at the geometric centre (or the average position) of the system.

Mention the position of the centre of mass of particles of equal mass.

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