The centre of mass of a body is located at the origin. The x -coordinates of the particles

Step-by-step solution

The x -coordinate of the centre of mass is given by X_ cm = m_i x_i m_i . Given X_ cm = 0 , we have m_i x_i = 0 . Since the mass of each particle is positive ( m_i > 0 ), the sum m_i x_i = 0 is possible only in two cases. First, x_i = 0 for all particles. In this case, all x -coordinates are zero, which means they are entirely non-negative. Second, some x_i > 0 and some x_i The x -coordinates cannot be entirely positive or entirely negative, as that would result in a non-zero centre of mass. Answer: could be entire