Suppose every particle of a body is positioned at a distance R from the origin. The distance of the body's centre of mass from the origin is

Step-by-step solution

Let the origin be O(0,0,0) . The position vector of the i -th particle of mass m_i is r _i . Given that every particle is at a distance R from the origin, we have | r _i| = R for all i . The position vector of the centre of mass is given by: r _ cm = m_i r _i m_i Taking the magnitude on both sides, we get: | r _ cm | = | m_i r _i m_i | Using the triangle inequality for vectors, | A _i | | A _i| , we have: | r _ cm | m_i | r _i| m_i Substituting | r _i| = R : | r _ cm | m_i R m_i | r _ cm | R m_i m_i | r _ cm | R Th