COMEDK 2025 Evening Solved Paper

Concept:The centre of mass is the point where the entire mass of a system can be considered to be concentrated. It depends solely on how the mass is arranged within the system.Explanation:The centre of mass of a system of particles with masses $m_i$ and positions $\mathbf r_i$ is given by$$\mathbf R_{\mathrm{cm}} = \frac{1}{M}\sum_i m_i\,\mathbf r_i$$where $M = \sum_i m_i$ is the total mass of the system.This formula clearly shows that $\mathbf R_{\mathrm{cm}}$ depends directly on the values of $m_i$ and their corresponding coordinates $\mathbf r_i$ — that is, on the mass distribution.Option B is incorrect because while the numerical coordinates of the centre of mass change when the origin is shifted, its physical location in space is independent of the choice of coordinate system.Option C is false because the shape and size of a body influence where the mass is distributed (e.g., a ring versus a disc of same mass); the centre of mass does depend on them through the distribution.Option A is not always true: a body may have translatory motion that does not preserve the relative positions of its parts (e.g., a rotating body in translation), so the centre of mass can change relative to the body itself.Hence, the fundamental and correct property is that the centre of mass depends on how the mass is spread or distributed within the system.Answer:Option D: Depends on the distribution of its mass.