Question

Which of the following are not correct about centre of mass ?
(1) It depends on frame of reference
(2) Internal forces may affect the motion of centre of mass
(3) Centre of mass and centre of gravity are synonymous
(4) In centre of mass frame momentum of a system is always żero

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (A)

1. Centre of mass of a body is independent of the frame of reference, eg, CM of a ring is at its centre whatever may be the frame of reference.
2. If ${\vec{F}}_{\text{ext. }}=0,{\vec{a}}_{CM}=0,ie,{\vec{v}}_{CM}=$ constant,
ie, if no external forces act on a system (or resultant external force acting on a system is zero) the velocity of its centre of mass remains constant. Hence, velocity of centre of mass is not affected by internal forces.
3. Centre of mass of a body is defined as the point at which the whole of its mass is supposed to be concentrated while centre of gravity of a body is defined as the point at which whole of its weight is supposed to be concentrated.
4. $\vec{p}=M{\vec{v}}_{CM}$
If ${\vec{v}}_{cm}=0,\vec{p}=0$ ie, in the frame of reference of centre of mass, the momentum of a system is zero.
So, options $(1),(2)$ and $(3)$ are the required options.