Question

If the net external force acting on the system of particles is zero, then which of the following may vary?

• A. Momentum of the sytem
• B. Acceleration
• C. Velocity of centre of mass
• D. Position of centre of mass

Answer 1

The correct option is D Position of centre of mass

According to the equation of motion of the centre of mas, $M{\overrightarrow{a}}_{CM}={\overrightarrow{F}}_{ext}$
If ${\overrightarrow{F}}_{ext}=0,{\overrightarrow{a}}_{CM}=0,$ i.e., ${\overrightarrow{v}}_{CM}=\text{constant}$
i.e., if no external force acts on a system (or resultant external force acting on a system is zero) the velocity of its centre of mass remains constant (i.e., velocity of the centre of mass is unaffected by internal forces). Hence, momentum of the system also remains constant.
So, if the centre of mass of a system is at rest (or in the state of uniform motion ), it will remain at rest (or in the state of uniform motion ) unless acted upon by an external force. Thus, if ${\overrightarrow{F}}_{ext}=0$, it is possible that the position of the centre of mass may change at a constant rate.