Question

The centre of mass of a system of two particles of masses $m_1$ and $m_2$ is at a distance $a_1$ from mass $m_1$ and at a distance $a_2$ from mass $m_2$ such that

• A. $\frac{a_1}{a_2}=\frac{m_2}{m_1}$
  
• B. $\frac{a_1}{a_2}=\frac{m_1}{m_2}$
  
• C. $\frac{a_1}{a_2}=\frac{m_1}{(m_1+m_2)}$
• D. $\frac{a_1}{a_2}=\frac{m_2}{(m_1+m_2)}$

Answer 1

The correct option is A $\frac{a_1}{a_2}=\frac{m_2}{m_1}$



Referring to diagram the distances of the centre of mass from masses $m_1$ and $m_2$ respectively are
And $a_1=\frac{m_{2}a}{(m_1+m_2)}$
$a_2=\frac{m_{1}a}{(m_1+m_2)}$
$\frac{a_1}{a_2}=\frac{m_2}{m_1}$
Hence the correct choice is (a).