Question

If the resultant of all 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. kinetic energy of the system does not change in time
C. angular momentum of the system does not change in time
D. potential energy of the system does not change in time.

Answer 1

Hint: An inertial frame is a frame where no acceleration is acting on the system. In an inertial frame, Newton’s second law holds true. Define Newton's second law in terms of the rate of change of momentum of the system. Then we can answer the given question.

Complete answer:
Inertial frame can be defined as a frame where the principle of inertia holds true. It can be defined as a frame which is not subjected under any acceleration.
In an inertial frame, Newton's second law of motion is valid. Newton's second law of motion states that the acceleration of the object is zero if the forces on the object are balanced or the net force on the object is zero.
In terms of the linear momentum, the second law can be expressed as, linear momentum of a system remains constant if the net external force on the system is zero.
Mathematically we can express it as,
$F={\displaystyle \frac{dP}{dt}}$
Now, if the force F is zero, the momentum of the system will not change with time or the rate of change of linear momentum will be zero.
So, if the resultant of all external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that linear momentum of the system does not change in time.

The correct option is (A).

Note:
According to Newton’s second law, an object will accelerate only if a net force or unbalanced force is acting on the system. If there is a net force acting on a system, the direction, velocity of the body can change. From the above expression we can simplify it as,
$F=ma$