Hello @JohnRennie sir

A rod kept on smooth horizontal surface

A force always perpendicular to rod end acts

Is velocity of cm zero

@PrateekMourya I've done this quetsion so i think i can answer in frame of centre of mass both the ends will have equal and opposite forces and centre of mass has net 0 velocity

I'm sorry the above case is when the the force has been removed in case the force is continuously acting the com has some acceleration + torque so velocity of com is not 0