Question

Which of the following is/are correct?

• A. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must also be moving.
• B. If centre of mass remains at rest, then net work done by the forces acting on the system must be zero.
• C. If centre of mass remains at rest, then the net external force must be zero.
• D. Internal forces cannot change KE of system.

Answer 1

Answer: (A), (C)

The correct options are
A If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must also be moving.
C If centre of mass remains at rest, then the net external force must be zero.

(a) As $\sum \overrightarrow{P}=0$ and $\overrightarrow{P_1}+\overrightarrow{P_2}\ne 0,\overrightarrow{P_3}$ cannot be zero.
(b) For any system of two or more than two particles, KE can change due to work done by internal forces while the centre of mass remains at rest.
(c) ${\overrightarrow{a}}_{CM}=0\Rightarrow \sum {\overrightarrow{F}}_{\text{ext}}=0$
(d) Internal forces cannot change momentum, but can change KE of system.