Question

The centre of mass of a system of particles is at the origin. From this we conclude that :

• A. The numberof particles on positive x-axis is equal to the number of particles on negative x-axis
• B. The total mass of the particles on positive x-axis is same as the total mass on negative x-axis
• C. The number of particles on X-axis may be equal to the number of particles on Y-axis.
• D. If there is a particle on the positive X-axis, there must be at least one particle in the negative X - axis.:

Answer 1

The correct option is D If there is a particle on the positive X-axis, there must be at least one particle in the negative X - axis.:

Given : The COM of the system is at origin i.e $X=0$

Let the position of particle of mass $m_1$ on the positive axis be $a$.

Using $X=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$\therefore$ $0=\frac{m_{1}a+m_2{x}_2}{m_1+m_2}$ $⟹x_2=-\frac{m_1}{m_2}a$

This implies that for a particle on the positive X axis, there must be at least one particle particle in the negative X axis.