Consider a two particle system with particles having masses m_1 a… - Vidyadip

MCQ

Consider a two particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the entre of mass through a distance $d$, by what distance should the second particle is moved, so as to keep the centre of mass at the same position?

A
$d$
B
$\frac{{m_2}}{{m_1}}$$d$
C
$\;\frac{{m_1}}{{m_1 + m_2}}$$d$
✓
$\;\frac{{m_1}}{{m_2}}$$d$

✓

Answer

Correct option: D.

$\;\frac{{m_1}}{{m_2}}$$d$

d
Initially,

$0 = \frac{{{m_1}\left( { - {x_1}} \right) + {m_2}{x_2}}}{{{m_1} + {m_2}}} \Rightarrow {m_1}{x_1} = {m_2}{x_2}\,\,\,\,\,...\left( 1 \right)$

Finally,

The centre of mass is at the origin

$\therefore 0 = \frac{{{m_1}\left( {d - {x_1}} \right) + {m_2}\left( {{x_2} - d'} \right)}}{{{m_1} + {m_2}}}$

$\begin{array}{l}
\Rightarrow 0 = {m_1}d - {m_1}{x_1} + {m_2}{x_2} - {m_2}d'\\
\Rightarrow d' = \frac{{{m_1}}}{{{m_2}}}d\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[Form\,\left( 1 \right).]
\end{array}$

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