Consider the following two statements:
(A) Linear momentum of a system of particles is zero
(B) Kinetic energy of a system of particles is zero
Then:
Solution:
When kinetic energy of the system is zero, speed of objects will be zero so momentum will always be zero.
Whereas momentum being a vector quantity may be zero when directions of velocities cancel each other. so speed and kinetic energy may of may not be zero when momentum is zero