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

Question

If the external forces acting on a system have zero resultant, the center of mass (A) May move but not accelerate (B) May Accelerate (C) Must not move (D) None of the above

Tardigrade Admin · Accepted Answer

According to the equation of motion of the centre of mass

M a_{CM} = F_{e x t}

If

F_{e x t} = 0, a_{CM} = 0

∴

v_{CM} = co n s t an t

i . e .

, if no external force acts on a system the velocity of its centre of mass remains constant. Thus, the centre of mass may move but not accelerate.

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

May move but not accelerate

May Accelerate

Must not move

None of the above

According to the equation of motion of the centre of mass MaCM​=Fext​ If Fext​=0,aCM​=0 ∴ vCM​=constant i.e. , if no external force acts on a system the velocity of its centre of mass remains constant. Thus, the centre of mass may move but not accelerate.

According to the equation of motion of the centre of mass
$M a_{CM} = F_{e x t}$
If $F_{e x t} = 0, a_{CM} = 0$
$∴$ $v_{CM} = co n s t an t$
$i . e .$ , if no external force acts on a system the velocity of its centre of mass remains constant. Thus, the centre of mass may move but not accelerate.