Question

how to show that if a force acting on a particle is zero its momentum will remain unchanged??

Answer 1

The second law states that the net force on a particle is equal to the time rate of change of its linear momentum p in an inertial reference frame:

where, since the law is valid only for constant-mass systems, the mass can be taken outside thedifferentiation operator by the constant factor rule in differentiation. Thus,

where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).
Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.

Answer 2

Answer:

According to Newton ' s second law of motion ,

F=d/dt When F=0, dp/dt = 0 or P = constant.

Explanation:

Force, F = dp /dt ( rate of change of momentum).Therefore, only when the momentum is constant, will the acting force be Zero.