Question

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that

• A. linear momentum of the system does not change in time
• B. the kinetic energy of the system does not change in time
• C. angular momentum of the system does not change in time
• D. the potential energy of the system does not change in time

Answer 1

The correct option is A

linear momentum of the system does not change in time

Inertial frame: An inertial frame is that in which the motion of a particle is not subject to forces and is in a straight line at a constant speed.

A diagram to represent the inertial frame:

We know that Newton's second law is valid in an inertial frame and the law states that,

Linear momentum remains constant if the net external force on the system of particles is zero.
$F_{resul\tan t}=\frac{dt}{dp}$

Hence$F_{resul\tan t}=0$, we can say that momentum of the system will not change with time.

Explanation for wrong answer:

If a couple force (equal in magnitude and opposite in direction) acts on the system

Net external force on system $\underset{F_{ext}}{\to }=+F-F=0$
However, w.r.t point A, a net moment of one of the forces F exists in a clockwise direction.
i.e, $\underset{{\tau }_{ext}}{\to }=0$
&$\underset{{\tau }_{ext}}{\to }=-\frac{dL}{dt}$
$-\frac{\underset{dL}{\to }}{dt}\ne 0$
∴$\underset{L}{\to }$≠constant
Hence angular momentum of the system can change with time, even though$\underset{F_{ext}}{\to }=0$.
For the K.E of the system to be constant, all collisions between the particles of the system should be elastic, and work done by any internal non-conservative forces should also be zero.
Hence options B and C are incorrect.

And we can see, that potential energy also changes as kinetic energy is not constant, option D is also incorrect.

So, option (A) is the correct answer.