Question

The sum of all the external forces on a system of particles is zero. Which of the following must be true for the system of particles?

• A. The total mechanical energy is constant
• B. The total potential energy is constant
• C. The total kinetic energy is constant
• D. The total momentum is constant

Answer 1

Answer: (A), (D)

The correct options are
A The total mechanical energy is constant
D The total momentum is constant

We know,

$\overrightarrow{F}=\frac{d\overrightarrow{p}}{dt}$

As $F_{net}=0$

There is no change in momentum,

Hence net momentum is constant.

And,

As $F_{net}=0$

There is no net work done on the system,

Hence no change in mechanical energy,

But mechanical energy=Kinetic+potential

Kinetic and potential energy can vary leading to a constant sum.

Hence $\text{A,D}$ is correct answer