Question

Centre of mass of a system of particles does not depend upon

• A. position of particles
• B. relative distance between the particles
• C. mass of the particles
• D. forces acting on the particles

Answer 1

The correct option is D forces acting on the particles

From the formula for the coordinates of COM of a system:
$x_{\text{COM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2},y_{\text{COM}}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2},z_{\text{COM}}=\frac{m_1{z}_1+m_2{z}_2}{m_1+m_2}$

$\therefore$ $x_{\text{COM}}$ or $y_{\text{COM}}$ or $z_{\text{COM}}$ only depends on the mass of the particles and the position of the particles. It will also depend on the relative position of the particles (i.e distance between them).

Position of $\text{COM}$ is independent of the forces acting on particles.