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(D) The position of the centre of mass $(R_{cm})$ for a system of particles is given by $R_{cm} = \frac{\sum m_i r_i}{\sum m_i}$.For two particles of

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For two particles of different masses,the centre of mass of the particles is nearer to the particle of lesser mass.

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(D) The position of the centre of mass $(R_{cm})$ for a system of particles is given by $R_{cm} = \frac{\sum m_i r_i}{\sum m_i}$.For two particles of masses $m_1$ and $m_2$ at positions $r_1$ and $r_2$,the centre of mass is closer to the heavier mass.Specifically,the distance of the centre of mass from $m_1$ is $d_1 = \frac{m_2}{m_1 + m_2} d$ and from $m_2$ is $d_2 = \frac{m_1}{m_1 + m_2} d$,where $d$ is the separation between them.If $m_1 > m_2$,then $d_1 Therefore,statement $(d)$ is incorrect as it claims the centre of mass is nearer to the particle of lesser mass.

Which of the following statements regarding the centre of mass is $NOT$ true?

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