When the resultant of all external forces acting on a system of particles is zero, we can apply the principles of conservation derived from Newton's laws of motion and from the understanding of mechanical energy to analyze the system. Option A, B, C, and D offer different statements about the system's properties, but only some of those are directly linked to the condition that the net external force is zero.
Option A: Linear momentum of the system does not change in time is true under the given condition. According to the law of conservation of linear momentum, if no external force acts on a system, the total linear momentum
p=mv (where
(m) is the mass and
(v) is the velocity of the system's center of mass) of the system remains constant. This arises from Newton's second law of motion, which in its integral form implies that the change in momentum of a system is equal to the impulse applied to it. If the resultant external force is zero, the change in momentum is also zero, so the linear momentum does not change over time.
Option B: Kinetic energy of the system does not change in time is not necessarily true. Kinetic energy is given by
‌mv2, where
(m) is mass, and
(v) is velocity. The change in kinetic energy can be zero in specific conditions of uniform rectilinear motion where no work is done by or against external forces. However, even if the net external force is zero, individual components of the system can still exert forces on each other, leading to internal work being done and changes in the kinetic energy of portions of the system.
Option C: Potential energy of the system does not change in time is not necessarily true either. Potential energy changes can occur due to internal forces within the system. For example, in a gravitational system, if two objects move closer together, the potential energy associated with their positions can change even if the net external force on the system is zero.
Option D: Angular momentum of the system does not change in time can be true if, in addition to the net external force being zero, there are no external torques acting on the system. Angular momentum conservation is contingent on the absence of external torques, similar to how linear momentum conservation depends on the absence of external forces. If no external torques are present (implied but not guaranteed solely by the condition that the net external force is zero), then the total angular momentum of the system remains constant over time according to the law of conservation of angular momentum.
Given the specific condition stated-namely, that the resultant of all external forces acting on the system is zero -the most directly and universally applicable statement is Option A: Linear momentum of the system does not change in time.