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(A) Let the two particles of masses $m_1$ and $m_2$ be placed at positions $x_1 = 0$ and $x_2 = d$ respectively on the $x$-axis.The formula for the ce

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at a distance $\frac{m_2 d}{m_1 + m_2}$ from $m_1$

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(A) Let the two particles of masses $m_1$ and $m_2$ be placed at positions $x_1 = 0$ and $x_2 = d$ respectively on the $x$-axis.The formula for the centre of mass $X_{cm}$ is given by:$X_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$Substituting the values:$X_{cm} = \frac{m_1(0) + m_2(d)}{m_1 + m_2}$$X_{cm} = \frac{m_2 d}{m_1 + m_2}$This distance is measured from the position of mass $m_1$ (which is at $x=0$).Therefore,the centre of mass is at a distance of $\frac{m_2 d}{m_1 + m_2}$ from $m_1$.

The centre of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $d$ is:

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