Question

The position of centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$ separated by a distance L apart, from $m_1$ will be

• A. $\frac{m_{1}L}{m_1+m_2}$
• B. $\frac{m_{2}L}{m_1+m_2}$
• C. $\frac{m_2}{m_1}\text{L}$
• D. $\frac{L}{2}$

Answer 1

The correct option is B $\frac{m_{2}L}{m_1+m_2}$

If follows from the figure that,
$X_{CM}=\frac{m_1\times 0+m_{2}L}{m_1+m_2}=\frac{m_2}{m_1+m_2}L$
$Y_{CM}=\frac{m_1\times 0+m_2\times 0}{m_1+m_2}=0$
$Z_{CM}=\frac{m_1\times 0+m_2\times 0}{m_1+m_2}=0$
i.e., the centre of mass is at a distance $\left[\frac{m_{2}L}{(m_1+m_2)}\right]$ from $m_1$ internally on the line joining the two particles.
Hence, the correct answer is option (b).