Question

The centre of mass of a system of two particles divides the distance between them

• A. in inverse ratio of square of masses of particles
• B. in direct ratio of square of masses of particles
• C. in inverse ratio of masses of particles
• D. in direct ratio of masses of particles

Answer 1

Answer: (C)

The position of centre of mass of system for n particles is expressed as
$R_{CM}=\frac{\Sigma m_i{r}_i}{\Sigma m_i}$
or $\Sigma m_i{r}_i=$constant
Hence, for a system having two particles, we have
$m_1{r}_1=m_2{r}_2$
$\Rightarrow \frac{r_1}{r_2}=\frac{m_2}{m_1}$
ie, the centre of mass of a system of two particle divides the distance between them in inverse ratio of masses of particles.