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(B) Let the positions of the two particles be $x_1$ and $x_2$ relative to the centre of mass $(CM)$.By the definition of the centre of mass,$m_1 x_1 =

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$m_1x/m_2$

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(B) Let the positions of the two particles be $x_1$ and $x_2$ relative to the centre of mass $(CM)$.By the definition of the centre of mass,$m_1 x_1 = m_2 x_2$.When the first particle is moved by a distance $x$ towards the $CM$,its new position is $x_1' = x_1 - x$.To keep the $CM$ at the same position,the second particle must be moved by a distance $x'$ towards the $CM$ such that $m_1(x_1 - x) = m_2(x_2 - x')$.Expanding this,we get $m_1 x_1 - m_1 x = m_2 x_2 - m_2 x'$.Since $m_1 x_1 = m_2 x_2$,these terms cancel out,leaving $-m_1 x = -m_2 x'$.Therefore,$x' = \frac{m_1 x}{m_2}$.

Two particles of mass $m_1$ and $m_2$ are separated by a distance $d$. If the first particle is moved towards the centre of mass by a distance $x$,then the distance by which the second particle must be moved towards the centre of mass to keep the centre of mass at the same position is:

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