An object of mass $3m$, initially at rest on a frictionless horizontal surface, explodes breaking into two fragments of mass $m$ and $2m$, respectively. Which one of the following statements after the explosion is true?

Kinetic energy of center of mass increases.

The smaller fragment will have twice the speed of the larger fragment.

Fragments have equal magnitude of momentum in ground frame but different magnitude of momentum in center of mass frame

Kinetic energy of system increases