Final answer:
To move both blocks with a combined mass of 12 kg across a frictionless surface, the force F will be equal to the tension in the string, which is 30 N.
Step-by-step explanation:
The question asks us to determine the force F required to pull two connected blocks across a frictionless surface, given the mass of the larger block is 8 kg, the mass of the smaller block is 4 kg, and the force of the connecting string on the smaller block is 30 N. Since the surface is frictionless and the system is presumably being pulled in a horizontal direction, the only horizontal force acting on the smaller block is the tension force provided by the string, which is 30 N. However, since both blocks are attached and moving together, and there are no other horizontal forces acting on the system, the magnitude of F will be equal to the tension in the string, since F is pulling the combined mass of both blocks. Therefore, the force F required to maintain the motion of the blocks across the frictionless surface is also 30 N.