Chapter 6 - Linear Momentum and Collisions - Learning Path Questions and Exercises - Multiple Choice Questions - Page 213: 16

(a) For a constant acceleration due to gravity, the center of mass and the center of gravity coincide.

Center of gravity is the point at which weight of the body is considered to be concentrated, where weight is the force exerted on the body by gravity. When the acceleration due to gravity is constant, the entire body experiences the same force. So, the center of gravity - \begin{align*} X_{CG}&=\frac{\sum (m_ig)x_i}{\sum(m_ig)}\\ &=\frac{g\sum m_ix_i}{g\sum m_i}\\ &=\frac{\sum m_ix_i}{M}\\ &=X_{CM} \end{align*}