Question

If the external forces acting on a system have zero resultant, the center of mass

• A. must not move
• B. must not accelerate
• C. may move
• D. may accelerate

Answer 1

Answer: (B), (C)

The correct options are
B must not accelerate
C may move

If the external forces acting on a system have zero resultant, then total momentum remains constant.
As $F_{ext}=\frac{dP}{dt}$
$\Rightarrow \frac{dP}{dt}=0$
$\Rightarrow P=$ constant
where $P=$ total momentum of the system

Hence if there is no external force, center of mass of the system either remains at rest or moves with a constant velocity.