Question

Assertion :If no external force acts on a system of particles, then the centre of mass will not move in any direction. Reason: If net external force is zero, then the linear momentum of the system changes.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

Acceleration of centre of mass ${\overrightarrow{a}}_{cm}=\frac{{\overrightarrow{F}}_{ext}}{M}$

If no external force acts on the a system of particles i.e. ${\overrightarrow{F}}_{ext}=0$

$⟹$ ${\overrightarrow{a}}_{cm}=0$

The acceleration of centre of mass is zero and so it will continue to move with its initial velocity.

Thus Assertion is incorrect.

rate of change of linear momentum of the system $\frac{d\overrightarrow{P}}{dt}={\overrightarrow{F}}_{ext}$

$\therefore$ $\frac{d\overrightarrow{P}}{dt}=0$ $(\because {\overrightarrow{F}}_{ext}=0)$

$⟹$ $\overrightarrow{P}=$ constant

Thus if no external force acts on the system, then linear momentum of the system is conserved.

So, Reason is incorrect.