If the resultant force on a system of particles is non-zero,...

If the resultant force on a system of particles is non-zero, then: (a) the linear momentum of the system must increase. (b) the velocity of the centre of mass of the system must change. (c) the distance of the centre of mass may remain constant from a fixed point. (d) kinetic energy of all particles must either increase simultaneuosly or decrease simultaneously.

If the resultant force on a system of particles is non-zero, then:
(a) the linear momentum of the system must increase.
(b) the velocity of the centre of mass of the system must change.
(c) the distance of the centre of mass may remain constant from a fixed point.
(d) kinetic energy of all particles must either increase simultaneuosly or decrease simultaneously.

Key Concepts

Work-Energy Theorem

The work-energy theorem relates the net work done by all forces (both external and internal) on a system to the change in its kinetic energy. For a system experiencing a net external force, the total kinetic energy of the system changes according to the work done, but the energy changes of individual particles do not necessarily occur uniformly. Internal forces and energy redistributions can result in situations where kinetic energy changes are not simultaneous for all particles in the system.

Center-of-Mass Motion

The center of mass of a system moves as if all of the mass of the system were concentrated at that point and all external forces were applied there. When there is a non-zero net external force, the acceleration of the center of mass is non-zero according to Newton’s Second Law. This implies that the velocity of the center of mass must change, although the position relative to a fixed point at some instants might remain constant.

Newton's Second Law for a System

This principle states that the net external force acting on a system equals the time rate of change of its total linear momentum. It is a fundamental concept in mechanics, meaning that if the resultant force is non-zero, the momentum of the system will change. This law applies to the system as a whole, regardless of the internal forces between its constituent particles.

Please give Ace some feedback