Question

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

• A. linear momentum of the system does not change with time
• B. kinetic energy of the system must not change with time
• C. angular momentum of the system does not change with time
• D. None of these

Answer 1

The correct option is A linear momentum of the system does not change with time

From Newtons's $2^{nd}$ law (valid in an inertial frame of reference),
${\overrightarrow{F}}_{ext}=\frac{\overrightarrow{dP}}{dt}$
If net external force on system is zero,
${\overrightarrow{F}}_{ext}=0$
Hence, linear momentum of system will remain constant.

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


Net external force on system ${\overrightarrow{F}}_{ext}=+F-F=0$
However, w.r.t point $A$, a net moment of one of the forces $F$ exists in clockwise direction.
i.e ${\overrightarrow{\tau }}_{ext}\ne 0...\left(i\right)$
$\&{\overrightarrow{\tau }}_{ext}=\frac{\overrightarrow{dL}}{dt}...\left(ii\right)$

From Eq $\left(i\right)\&\left(ii\right)$:
$\frac{\overrightarrow{dL}}{dt}\ne 0$
$\therefore \overrightarrow{L}\ne \text{constant}$
Hence angular momentum of system can change with time, even though ${\overrightarrow{F}}_{ext}=0$.

For $\text{K.E}$ of 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, option A is correct.