Consider a two particle system with the particles having masses `m_1 and m_2`. If the first particles pushed towards the centre of mass through a distance d, by what distance should the second particle be moved so as the keep the centre of mass at the same position?

Explanation

To solve the problem, we need to determine how far the second particle (mass \( m_2 \)) must be moved in order to keep the center of mass of the two-particle system in the same position after the first particle (mass \( m_1 \)) is pushed towards the center of mass by a distance \( d \).

### Step-by-Step Solution:

1. **Define the Center of Mass (CM)**:
The center of mass \( x_{cm} \) of a two-particle system is given by the formula:
\[
x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}
...