Question

A system consists of mass M and m (<< M). The centre of mass of the system is

• A. at the middle
• B. nearer to M
• C. nearer to m
• D. at the position of larger mass

Answer 1

The correct option is B nearer to M

Distance of the centre of mass from mass $m_1$ considering $m_1$ to be placed at origin is .
$X_{CM}=\frac{m_2}{m_1+m_2}L$
Hence, its distance from mass $m_2$.
$X_{CM}^{\prime }=1-X_{CM}=\frac{m_1}{m_1+m_2}L$
Hence, $\frac{X_{CM}}{X_{CM}^{\prime }}=\frac{m_2}{m_1}$
Suppose, $m_1=M,m_2=m$
then $X_{CM}<X_{CM}^{\prime }$
i.e., Distance of COM wrt mass M < Distance of COM wrt mass m
i.e., COM lies nearer to M.
Hence, the correct answer is option (b).