Can objects in a system have momentum while the momentum of the system is zero? explain your answer.

Yes. Momentum is a vector, so several non-zero momenta can add up to zero. Consider for a simple example a mass of 10kg moving to the right at 5m/s, and another mass of 10kg moving to the left at 5m/s. These momenta each have a magnitude equal to 50 kg m/s but have opposite sign and so the total system's momentum is zero.