Question

The centre of mass of a system of two particles of masses $m_1$ and $m_2$ is at a distance $d_1$from $m_1$ and at a distance $d_2$ from mass $m_2$ such that

• A. $\frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}}$
• B. $\frac{d_{1}}{d_{2}} = \frac{m_{1}}{m_{2}}$
• C. $\frac{d_{1}}{d_{2}} = \frac{m_{1}}{m_{1}+m_{2}}$
• D. $\frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}+m_{2}}$

Answer 1

Answer: (A)

Refer figure. The distances of centre of mass $CM$ from masses $m_1$ and $m_2$ are
$d_{1} = \frac{m_{2}d}{m_{1}+m_{2}}$ and
$d_{2} = \frac{m_{1}d}{m_{1} +m_{2}} $
$ \therefore \frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}}$