Two blocks of masses m1 and m2 being connected with a light spring of stiffness k are driven with forces F1 and F2 on a smooth horizontal plane. If the blocks move with same acceleration a0,  the value of a0 is:

In the given system, the spring force due to spring on the masses is internal force. The acceleration of system is due to external forces only. Here we can assume the two blocks as one system and their acceleration is given asa0= Net force towards motion of masses  Total mass a0=F1-F2 m1+m2a0=F1-F2 m1+m2