Answer
1) a
2) b
Work Step by Step
a) The skaters are moving in a straight line together, so clearly their center of mass has a velocity. However, they remain together, so there is no internal kinetic energy.
b) The momentum of the system is conserved since no outside work is done. Since they are initially at rest, even though there is kinetic energy internal to the system, the overall kinetic energy must be 0 since no work is done on the system.
c) This is like b), except since the system initially is moving, the CM of the system has kinetic energy as well after they push off.
